Math Problems
The sum of two times the square of a number and five times that number is thirty-three. What is the number? A 1 B 2 C 3 D 4 E 5
2x^2 + 5x = 33 2x^ - 6x + 11x - 33= 0 2x(x-3) 11 (x-3) x= -11/2 x= 3
Susan earns $24/hr at her full time job for the first 40 hours. She can world overtime and earn an hourly rate of 1.5 times her normal pay rate. What is susans salary if she works 56 hours this week?
$24 x 40hr = 960 $24 (1.5) x 16hr = 576 960+576 = 1536
if x^2 + 2xy + y^2 = 81 and 2r + 3s = 3, which of the following is correct? CA CB x+y 4r^2+12rs+9s^2
(x+y)^2 is equal to the equation in the problem. and (2r+3s)^2 is equal too the equation in column B.
How much more does jane pay for utility bills than for food per month? Utility 18% Rent 30% Other stuff 17% Food 15% Insurance 20% A $90 B 130 C 200 D 250 E 300
.18 x 3000 = 540 .15 x 3000 = 450 540 - 450 = 90
If b is 60% of x and d is 5/8 of x, what is the value of b/d?
0.6(x)/ 5/8x cancel x's. the multiple by 8 to cancel fraction. mutiply by 10 since a decimal. 24/25
Rebecca has $100. She buys a movie tickets for 11.50 and spends 15.31 on lunch. She receives 50 from her mother and buys 3 shirts for 13.50 each. How much money does rebecca have left over?
100 - 11.50 - 15.31 = 73.19 73.19 + 50 = 123.19 123.19 - 3(13.50) = $88.69
A car travels 108 miles in 4 hours. How many miles can it travel in 9 hours at this same rate? A 175 B 201 C 243 D 271 E 300
108/x = 4/9 4x = 972 x= 243
What is the ratio between the amount jane pays for food and for insurance? Utility 18% Rent 30% Other stuff 17% Food 15% Insurance 20% A 3:4 B 1:2 C 2:1 D 4:3 E 20:15
15%/20% 15:20 reduce 3:4
The pie chart below shows the distribution of Janes expensive which is 3,000 per month. Based on this info, how much does jane pay in rent each month? Utility 18% Rent 30% Other stuff 17% Food 15% Insurance 20%
3000 x .3 = 900 to rent
Ricky can paint a room in 4 hours and marly can paint it in 6 hours. What percent of the job does marly do it she is working together with ricky?
40% for marly
A bag contains 5r, 4g, 8b, 3y marbles. What is the probability of selecting a green or yellow marble on the first try?
4g + 3y = 7 total marbles. 7/20 answer * "or" means add
John has 5 books that he wishes to place in order in his shelf. In how many different ways can john arrange his books? A 20 B 25 C 60 D 120 E 180
5 factorial to find the answer 5! = 1 x 2 x 3 x 4 x 5 = 120
Mark is deciding what clothes to put on. he has 5 different pants, 7 different shirts, and 4 different types of shoes. If he uses one from each, how many combos can he make?
5 x 7 x 4 = 140
When five times the difference of a number and seven is divided by three, the result is ten. What is the number? A 4 B 5 C 7 D 10 E 13
5(x-7)/3 = 10 times 3 to cancel. 5(x-7) = 30 divide by 5 to cancel. x - 7 = 6 x= 13
If the average of eight numbers is 52 and the average of five of these is 46, what is the average of the other three number? A 54 B 57 C 59 D 62 E 65
52(8) = 46(5) + x(3) x= 62
A bag contains 5 red marbles, 4 green marbles, 8 blue marbles, and 3 yellow marbles. What is the probability of selecting a red marble at random?
5r + 4g + 8b + 3y = 20 total 5/20 is reduces to 1/4.
A car travels 60 mph for 3 hours and then 50 mph for 5 hours in the same direction. What is the average speed of the car during this trip?
60mph x 3hrs = 180 50mph x 5hrs = 250 180+250 = 430 5hrs+3hrs= 8 430/8 = 53.75
A car travels at a speed of 60mph for 5 hrs. It makes the return trip in 4 hours. What is the average speed of the car?
60mph x 5hrs = 300 miles xmph x 4 hrs = 300 miles total trip 300+300= 600 600miles/9hrs = 66.7
If seven more than four times a number is eight less than that number, what is the number? A 11 B -7 C 14 D -5 E 12
7 + 4x = x -8 =-5 remember that if it says (n less than that number) to make it backwards.
There are seven drivers in a race. How many different permutations are possible if there are only 4 winners? A 200 B 365 C 510 D 720 E 840
7! ---- (7-4)! =840
Of all the cars in a certain community, 70% are blue. 80% of the blue cars have 4 doors. IF there are 28 blue cars that do not have 4 doors, how many cars are there in this community? A 60 B 88 C 112 D 140 E 200
= 200 total
A certain vehicle can travel 125 miles using 6 gallons of gasoline. How many gallons of gasoline are required to make a trip if 1500 miles?
A 54 B 65 C 72 D 83 E 96
There are 500 marbles in a jar consisting of red, blue, and grenn marbles. 16% are blue and 14% are green. How many marbles are in this jar?
B = 16% G = 14% 16% + 14% = 30 100%-30% = 70% r=70% 500(.7) = 350
Consider the following list of numbers 12 17 21 22 22 26 30 36 42
CA= Mean CB= Median a A> b B> c A=B d No relation
What is the slope of the linear equation 2x - 5y = 10?
Change into y-intercept form. y=mx+b. 2/5 is slope A 5 B 5/2 C -2/5 D -5/2 E 2/5
A car traveling east at 40mph and a bus is traveling west at 30mph. The two vehicles are currently 350 miles apart. How long will it take until they pass each other?
Dc + Db = 350 40t + 30t = 350 t = 5hrs
Jason buys 45 bags of flour for x dollars. At the same rate, how much would it cost to buy 72 bags of sugar?
IF given a smaller value first and then asked to find y of a larger number, the bigger number goes ontop. 8x/5 A 8x/5 B 9x C 5x/8 D 5x E 5/8x
If 91 shirts cost x dollars, then how much do 49 shirts cost in terms of x?
If the first number is given is larger than the second number, the larger number goes on the bottom. 7x/13 A 7x B 7x/13 C 13x D 13x/7 E 21x
Julian, steve and darcy are going to buy a big tv for 2,400. If darcy pays 100 more than steve and julian pays 700 more than twice as much as steve, then how much does steve pay? A 300 B 400 C 500 D 700 E 800
J + S + D =2400 d= 100 + S j = 700 + 2s 700 + 2s + s + s + 100 = 2400 s= 400
IF x+2y= 13 and 3x-2y= -1, what is the value of 5x+4y
Line up the two equations and combine to find x. Take x and plug into one of the orgianl equations, solve for y. Plug x and y into the last equations and you get your answer.
7 apples and 5 bananas cost $6.30. 11 apples and 7 bananas cost $9.60. Based on this info, how much will 15 apples and 13 bananas cost?
Multiple each equations by the opposite B variable to get the Bs to cancel. Solve for A. Then plug into the first equation to get B. Then take A and B and plug into final equation for answer. A 12.30 B 13.80 C 14.30 D 14.90 E 15.70
How many ways can we select 3 memebers from a club of 10 students to fill the role of president, secretary, and vice presiedent?
No order = nCr 10C3= 10!/ (10-3)!(3)!
Saharon is one more than four times tinas age. 4 years from now, sharon will be seven more than twice tinas ago. How old will sharon be 9 years from now? A 15 B 19 C 24 D 28 E 30
Present: S & T Future: S + 4 & T + 4 s= 1 + 4t s + 4 = 2 (t + 4) + 7 t= 5. s= 1 + 4(5) s= 21
The ratio of boys to girls in a class of 400 students is 2 to 3. How many boys are in this class?
Set up a proportion x/2 = y/3 = 400/5 put boys to total. Cross multiply and solve for x. 160 boys A 160 B 200 C 240 D 260 E 300
Sarah can paint 2/9 of an entire house using 3 cans of paint. How many cans of paint are required to finish the rest of the house.
Set up a proportion of Cans to Fraction. multiple by the denominator to cancel. Then solve for x. x= 10.5 cans of paint.
z liters of water flow into a bucket every x minutes. At some rate, how many liters of water flow into a bucket every minute?
Set up a proportion of Liters to Minutes. L/Z = Y/X xl=yz, solve for L. YZ/X A Y/XZ B XY/Z C XZ/Y D YZ/X E Z/XY
It takes john 3 hours to pain 15% of a house. How long will it take him to finish painting the rest of the house?
Set up a proportion of Time to percent. Put what % is left on the bottom. Cross multiple and then solve for X. x= 17 hours.
It takes mary 5 hours to collect 150 apples and it takes Sarah 7 hours to pick 140 apples. How many apples can they collect in 12 hours if they are working together?
Set up individual proportions to find how many each can do in 12 hours. Then add the two numbers together. 600 A 420 B 490 C 525 D 570 E 600
Which of the following values of x is a solution to the equation x^2 - 2x = 15?
Set up to factor to find x. x^2 - 2x - 15 = 0 (x+3) (x-5) = 0 x= -3, 5 A -5 B -3 C 0 D 2 E 3
Which of the following values of x is a solution to the equation 6x^2 - x - 12 = 0. Select all that apply
Since lead coefficient is greater than 1. We must multiply it by the last number and add the 2 numbers that equal -1 into the equation. then spilt into two and factor. A 1/3 B 3/2 C -2/5 D 2/3 E -4/3
Gabby average score for seven tests is 95. If the sum of two test is 180. then what is the average for the other five test? A 94 B 95 C 96 D 97 E 98
Sof7 = s2+s5 95(7)= 180 + x(5) x= 97
What is the value of x in the equation shown below? Select all that apply. 2(8x + 3) + 7 = 97 A 4.1 B 21/4 C 5.25 D 19/2 E 5 & 1/4
Solve by x with order of operations. x = 21/4 or 5.25 or 5 & 1/4 21/4 is an imprper fraction, it can be made into a mixed number. B, C
Which of the following could be a value of x? Select all that apply 2(5 - 3x) >_ -14 A 19 B 12 C 6 D 4 E 1
Solve for x. x <_ 4 You must flip the sign when multiplying by a negative. d,e
Laura can complete a task in 15 hours. roger can do it in 10 hours. How many minutes will it take them to complete 2/5 of the task working together?
T= 144min.
Juliet can clean an entire house in 10 hours. It takes sonia 15 hours to do the same job but it only take roger 3 hours to complete the same task. How long will it take to clean the entire house if they all work together?
T= 2
John can paint a room in 40 minutes. Jared can do the same job in 2 hours. How long will it take them to paint a room working together?
T= 30 minutes.
Megan can paint an entire house in 6 hours. Joe can do it 12 hours. How long will it take megan and joe to paint the entire house working together?
T= 4
How long will it take a car moving at 65mph to travel a distance of 845 miles? A 9 HRS B 11 HRS C 12 HRS D 13 HRS E 14 HRS
T= D/S 845/65 = 13
The price of a certain stock is $100. In one month, the stock rises 50%. Two months later, it dorps by 50%. What is the final price of the stock?
Take $100 and increase by 50% (1.50). you get 150, then decrease by 50% (0.5) is $75 dollars.
A jar contains 30 marbles consisting of red and blue marbles only. If there are 6 more red marbles than blue marbles, how many red marbles are there?
Take R+B= 30 and then B+6=R and plug R into first equation. you then get number of B=12 A 6 B 12 C 18 D 20 E 24
Lisa can complete a task in 6 hours. Lisa and David can complete the same task in 2 hours working together. How long will it take David to complete the task if he works by himself?
X= 3
A bag contains 5r, 4g, 8b, 3y marbles. What is the probability of selecting a blue and a green marble with replacement?
be careful b/c order is not specified. means it could be green OR blue. Get ratios and then add them together. B, G 2/5 x 1/5 = 2/25 G,B 1/5 x 2/5 = 2/25 2/25 + 2/25 = 4/25
A bag contains 5r, 4g, 8b, 3y marbles. What is the prp[ability of selecting Blue on the first try and green on the second with replacement?
blue is 8/20 reduce to 2/5. green is 4/20 reduce to 1/5 *"and" means multiply
In a certain month, jane decides not to spend anything on misc stuff. what percentage of her expenses is due to insurance this month? Utility 18% Rent 30% Other stuff 17% Food 15% Insurance 20%
find .17 of original amount. subtract that from 3000. then take dollar amount of insurance % at 20% then divide by 2490 and you get your answer 24.1%
Sarah has taken 4 chemistry tests and has an average score of 82. If she scores a 97 on her next test, what is her average score for these five tests? A 83 B 84 C 85 D 87 E 90
find the sum of the first tests and add 97 to it and divide by 5. = 85
The surface area of a sphere is 144pie. What is the volume of the sphere?
first, solve for r in surface area, plug 144 pie into that. Then take r and plug into volume equation. 288pie or 904.78
If f(x,y) = 3x^2 - 6y, and f(2,y) = -6 , and f(x,2) = 63, which of the following statements is true? CA CB x y
no relationship.
#99. A jar contains 30 coins consisting of nickels, dimes, and quarters. The total value is $3.95. If there are 5 more dimes than nickels, how many quarters are in the jar.
number of quarters 9
CA CB f(x)= 7x+5 f(3) f(x)= 100 A A> B B> C A=B D No relation
plug 3 into the equation. Then replace f(x) with 100 on 7x+5 then solve for x.
If the volume of a cube is 64 ft ^3, what is the surface area of the cube.
plug 64 into the volume equation, then take x and plug into surface area. sa=96
The sum of a list of positive numbers equals 4 times the average (arithmetic mean) of the numbers. How many numbers are in the list?
plug into the average formula then solve for n. N=4a ---- n
Bonny is five years younger than roger and four times as old as dana. If dana is d years old, how old is roger in terms of d? A 4d + 5 B 5d+ 4 C 4d - 5 D 5d - 4 E d +5
put the two equations from the wording and set them equal to each other. and then solve for R. 4d + 5
A bag contains 5r, 4g, 8b, 3y marbles. What is the probability of selecting a red marble on the first try and yellow on the second, without replacement?
red is 5/20 reduce to 1/4 yellow is 3/19 1/4 x 3/19 = 3/76
If 40% of x is 80 and 30 is y% of 5, which of the following statements is true? CA CB x y
remember when solving for second equation that we are finding the percent so you much x by 100 at the end.
Company ABC has 200,000 to spend on the advertising department, the research department and the sales department. If 1/4 of the money goes to the advertising department and 1/3 of the remaining money goes to the sales department, how much money is left for the research department?
research= 100,000 200,000/ 1/4 = 50,000 200,000 - 50,000 = 150,000 150,000 / 1/3 = 50,000 150,000 - 50,000 = 100,000
Lisa had read 230 pages of a book over the weekend. If on saturday, she read 80 pages more than half the amount she read on sunday, how many pages did she read on saturday? A 155 B 130 C 100 D 90 E 75
saturday is X and sunday is Y. x + y =230 she read 80 pages more than half the amount she read on sunday. x= 80 + 1/2y 80 + 1/y + y = 230 y + y =300 y= 100 x+100 = 230 x= 130
Mary can make 12 cupcakes in 5 minutes. How many cupcakes can she make in 2 hours?
set up a proportion or turn into minutes, and how sets of 5 min are in 120. multiply 12x24 to get 288 cups cakes in 2 hours. A 324 B 288 C 270 D 244 E 176
A laptop sells for $399. A customer uses a 15% discount after which a sales tax of 8% is applied. How much money will they spend?
take 15% from 399 then add 8% to that number, and you get your answer $366.28 A 361.49 B 266.28 C 371.19 D 374.32 E 379.83
A student uses a 10% coupon to reduce the price of a textbook. With a sales tax of 7%, the student pays a final amount of $216.68 for the textbook. What was the original price?
take 7% (1.07) sales tax and divide by price paid. Then take that number and divide by 10% (1-.10= .90) to get original selling price $225 A 220 B 230 C 210 D 225 E 215
Which of the following is not a composite number? A 12 B 35 C 19 D 4 E 21
test each answer to see if it have factors others than 1 and itself. c 19
Which of the following is equivalent to 1.75? Select all that apply. A 5/4 B 21/12 C 7/4 D 9/5 E 1 & 3/4
turn into a mixed number, then from a mixed number into a fraction. Then try answers and simply. 1 & 3/4, 21/12, 7/4
The dimensions of the rectangular box is shown below are 4in x 5in x 6in. What is the volume and total surface area of the box?
v = 120 sa = 148
Calculate the volume and total surface area of the cone that has a radius of 5in and a height of 12in.
v= 100 pie sa= 90pie
The sum of four consecutive even integers is 84. What is the product of the second and third integer? A 360 B 390 C 420 D 440 E 482
x + (x+2) + (x+4) + (x+6) = 84 4x + 12 = 84 x=18 18 + 20 + 22 + 24 = 84 product of second and third integer? 20 x 22 = 440
The sum of three consecutive positive even integers is z. In terms of z, what is the sum of the first and second integers? A 2z-4 B 3z-2 C 2z-10/3 D z/2-3 E 2z-6/3
x + (x+2) + (x+4) = z x = z-6/3 plug x into the first and second and find the sum. 2x-6/3 plug
The sum of three consecutive integers is 42. What is the sum of the first two integers? A 20 B 27 C 29 D 42 E 31
x + x + x = 42 x + (x+1) + (x+2) = 42 Solve for x x=13 13 + 14 + 15 = 42 First two 13 + 14 = 27
The ratio of red and blue marbles in a jar is 4 to 9. If there are 104 marbles in the jar, how many of them are red?
you know r + b = 104 and that r/b = 4/9 solve for b in the r/b then plug into r + b = 104. then solve for r.