HESI Math 5

(5 + x) (5 - x)

Answer: (25-x2) Explanation: First - OUtside- Inside - Last First: 5x5 =25 Outside : -5x Inside: 5x Last: -x2 Combine 25 + -5x + 5x - x2 = 25- x2 (answer)

23/12 - 45/3 =

Answer: - 13 1/12 Explanation: This is another complex fraction that will take too much of your time to find a common denominator. Instead long divide each fraction so that you have two decimal numbers that you can use. Notice that 3 goes into 45 more times than 12 goes into 23, so the answer will be negative.

34x - 2xy ( 34x + 2xy) - 32x ( 3x) - 44x

Answer: -2x [ 48x + 34xy +2xy2 + 5] Explanation: None of the items in parentheses can be combined. When multiplying by the number outside of the parentheses, remember that "x times y"= xy and that "x times x" = x2

4 3/7 - 7 34/9 =

Answer: -6.34 Explanation: These are two mixed numerals. Change each of the mixed numerals into an improper fraction, then divide the denominator into each numerator so that you have two decimals which you can then subtract. But always be sure that you know if the answer will be negative or positive. Once you can see which decimal is bigger, just do the subtraction as a normal subtraction problem and then apply the negative sign.

0.245/ 234

Answer: 0.00104 Explanation: To make this division easier, 0.245 can be written as 245 x 10 ^-3 (10 to the power negative 3), then perform the division.

What is 30% of 657?

Answer: 197.10 Explanation: Multiply 0.30 time 657

There are 400 students in the school, 34% of them are all A students, 44% are all B students, and the rest are all C students. How many C students are there?

Answer: 88 Explanation: Add up all the percentages, 34 + 44 = 78, this leaves a percentage of 22 to make 100. Next, take 0.22 x400 to find the C students.

Two angles of a triangle have the following measurements, 30 degrees, and 60 degrees. What is the measure of the third angle?

Answer: 90 degrees Explanation: All angles of a triangle must add up to 180 degrees, therefore given two of the angles you can find the third by subtracting the sum of the two angles from 180.

-9 1/12 - 6 1/4 =

Correct answer: -15.33 Explanation: This problem requires that you know how to use the negative sign. Here we are adding two negative mixed numerals. First turn each mixed numeral into an improper fraction and then long divide the denominator into each numerator.

Solve for x: 3(3/4)x + 23x + 45/6 = 3

Correct answer: -18/101 Explanation: First 45/6 can be reduced to 15/2. Combine all like terms and solve for x.

4 7/8 - 34 12/5 =

Correct answer: -32 Explanation: These are mixed numerals. The first step is to turn them into improper fractions. This is a fraction that has a larger numerator than the denominator. To do this multiply the denominator to the whole number and add that answer to the numerator. This will give us 39/8 and 171/5. It is easy to see that the answer will be negative since 5 goes into 171 more times than 8 goes into 39. Now just long divde each denominator into the numerator and perform the operation.

Solve for x : 32x - 2.4y + 16x = 15 + z

Correct answer: 15/48 + z/48 + y/20 Explanation: The key is to get all of the "x" containing numbers on one side and the other variables on the other side of the equal sign. combine 32x+16x = 48x, Add 2.4y to both sides and then divide the entire equation by 48. 48x/48 = 2.4y/48 + 15 /48+ z/48 x = 2.4y/48 + 15/48 + z/48, now just reduce the fraction 15/48, ALWAYS REDUCE ALL FRACTIONS TO LOWEST TERMS

¼(x) -1/8(x) = 3 - 1/16(x)

Correct answer: 16 Explanation: ¼(x) -1/8(x) = 3 - 1/16(x) 16{1/4(x) -1/8(x) = 3 - 1/16(x)} Now distribute the 16 to each of the items within the parentheses So now we have.... 16(1/4)x - 16(1/8)x = 16(3) - 16(1/16)x O.K., do you see what is going on? We are simply multiplying a whole number times a fraction right? So how do we multiply a whole number times a fraction? Answer: Numerator times the numerator and the denominator times the denominator. But what if our number doesn't have a denominator? No problem, we just put a 1 under the number. It doesn't change the number does it? No, of course not. So..... 4x - 2x = 48 - x do you see how we came up with these numbers? Well if you get your calculator and multiply 16 and ¼ or 0.25 you should get 4 and 4 times x is 4x. Just like the rest of the items in the equation, the denominator goes into the numerator., so 8 divides into 16 and 16 divides into 16 to get 1. Now we can easily solve for x. First combine like terms on both side of the equation. 4x -2x = 2x = 48 -x 2x = 48 -x ( now we must eliminate the x next to the 48, so that numbers are on one side of the equal sign and letters or variables are on the other. Let us add a positive x to both sides of the equation. 2x +x = 48 -x + x 3x = 48 (now divide (opposite of multiplication) 3 by both sides of the equation. 3/3 (x) = 48/3 (x) = 16 now put this back into the equation to verify that it works.

When Mike is 18 years old, Mary is half his age. How old is Mary when Mike is 30 years old?

Correct answer: 21 Explanation: If Mary is half of Mike's age when Mike is 18 years old, the Mary is 9. She will always be 9 years younger than Mike, even when Mike is 30.

0.000567/0.00589

Answer: 0.096 Explanation: The best way to tackle this problem is to first turn each number into a factor of ten, then divide the numbers. (567 x 10-6 )/(589 x10-5 ) Long divide 589 into 567 and then use the rules of exponents for the factors of 10, 10-6-(-5) = 10-1

389 is what percent of 27,689?

Answer: 1.4% Explanation: Use the key words. 389 is(=) x (what) ( 27,689) is (implies equals) what( implies the variable x) of ( implies the operation of multiplication) Setting this problem up requires that we divide both sides by 27,689. That leaves "x" by itself and then divide 27,689 into 389. Don't take it out to more than the thousandths place. You will be able to discern the answer from the choices given.

3/6 + 2/7 =

Answer: 11/14 Explanation: When adding, subtracting, multiplying or dividing fractions, always look for the fractions that can be reduced before performing any operations. For instance, in this problem we can see that 3/6 reduces to 1/2. Now all we have to do is find a common denominator that both 2 and 7 can divide into evenly. That would be 14. Now we construct two equivalent fractions. To do this we must simply divide both the 2 and the 7 into the number 14 and multiply the resulting number with the numerator. So our new equivalent fractions become, 7/14 + 4/14 = 11/14

3 runners out of 10 runners is the same as _____________ runners out of 50.

Answer: 15 Explanation: This is a ratio and proportion problem. Set it up as follows: 3/10= x/50 and solve for x by multiplying both sides by 50

16 marbles out of 27 marbles is similar to 12 marbles out of _____________.

Answer: 20.25 Explanation: Set it up: 16/27 = 12/x Solve for x, since x is in the denominator, we must first get x in the numerator. So begin by rewriting the ratio, 27/16 =x/12, now multiply each side by 12.

Bill makes three times what Dave makes in two days. Dave makes 50% less than Peter in two days. If Peter makes $100 per day, how much does Bill Make?

Answer: 300 Explanation: (Dx2)/3 =B 2xD=(Px2) These equations were set up as equalities. Now substitue 100 for P, solve for D, then substitute D and solve for B.

The measurements of a shape are as follows: 12 feet, 13 feet, 2 feet and 6 feet. What is the perimeter?

Answer: 33 ft Explanation: Perimeter implies to add up all of the sides.

(24/0.45) x 65 + 3/4

Answer: 3467 Explanation: Perfom the division within the parenthesis, then the multiply, then the add.

27 is what percent of 67?

Answer: 40.3% Explanation: 27 = x(67), solve for x by dividing both sides by 67.

What percent of 78 is 34?

Answer: 43.6% Explanation: x(78) = 34, solve for x by dividing both sides by 78. Then multiply by 100.

15% of all basketball players at a college practice 3 hours per day, 25% practice 4 hours per day and the rest only practice for 1 hour daily. What is the number of players that practice for 1 hour per day, given that there are 75 basketball players on the team.

Answer: 45 Explanation: Add up the percentages, 15 + 25 = 40, and 100-40=60 Therefore take 0.60x75

Jake rode his bicycle at 10 miles per hour, to a store one mile down the road. How long did it take Jake to arrive at the store?

Answer: 6 minutes Explanation: Distance = rate x time 1 mile = 10mi/hr (x) 0.10 hr x 60min/1hr = 6 min

324 out of 1000 is similar to 21 out of _____________.

Answer: 65 Explanation: 324/1000 = 21/x re-write so that x is in the numerator 1000/324 =x/21, multiiply both sides by 21.

Round your answer to the nearest whole number. 22.67 x 3.3 =

Answer: 75

78 is what percent of 900?

Answer: 8.67% Explanation: 78 = x(900), solve for x by dividing both sides by 900

3 - 7 1/8 - 3/9 =

Correct answer: -4.458 Explanation: Here you must combine a whole number, a mixed number, and a fraction. Reduce if possible. First, 3/9 reduces to 1/3, then turn the mixed number into a fraction 57/8, and then find a common denominator for 1,8, and 3, which is 24. Notice that the denominator for the 3 or for any whole number is always a 1. Keep track of your negatives and positives. Here, you will add two negative numbers and then add a positive number. The number that is the biggest will determine the sign. For instance -89 + 8= -81, this is because there are more negative numbers that make -89 than make +8.

5.6/78.9 + 35/8 - 67 + 1 1/4

Correct answer: -61.3 Explanation: The best way to tackle this problem is to turn all fractions into decimals and then perform the addition and subtraction.

4(5x -7) = -56

Correct answer: -7/5 Explanation: 4(5x -7) = -56 How to solve? The first thing that we must do is to see if we can solve or combine like terms in the parentheses. Answer is no we cannot. Next we use the distributive property of multiplication to distribute the 4 to each of the items within the brackets. So we have.... 4(5x) -4(7) = -56 Which gives us.. 20x -28 = -56 now we must add 28 (which is the opposite of -28) to both sides of the equation. 20x -28 + 28 = -56 +28 20x = -28 (remember that when you are adding or combining two signed numbers, take the difference just like you would a normal subtraction problem, but keep the sign of the number that is the largest. In our case a negative. Now let's solve for x by dividing both sides by 20 20x/20 = -28/20 (x) = - 7/5 or - 1 2/5

Susan gained 30 pounds during her last trimester of pregrancy. How many pounds per day did Susan gain? You can assume each month has 30 days.

Correct answer: 0.33 lb Explanation: A trimester is 3 months. So Susan gained 30 lbs in 3 months. There are 30 days in a month, or 90 days in three months, or 10 pounds in one month or 10 lb/30 day, reduces to 1/3 = 0.33 lbs per day.

If Brad can walk 10 miles in 5 hours, how far can he walk in 30 minutes?

Correct answer: 1 Mile Explanation: 30min x10mi/5hrx 1hr/60min = units hours and minutes cancel leaving miles.

(57 x 2/3)/24

Correct answer: 1.6 Explanation: Multiply the items in parenthesis first, then divide by 24

5/6 + 7/9 =

Correct answer: 1.6 Explanation: Since we can't reduce any farther, find the common denominator, which is 18 and construct two new equivalent fractions and then add.

104/120 - 44/55 =

Correct answer: 1/15 Explanation: Remember, don't get nervous when you see these large fractions. The first step is to see if you can reduce them into smaller fractions. 44/55 reduces to 4/5, and 104/120 reduces to 13/15. In this form the fractions are easier to use. Now find the common denominator, which is 15, and construct two new equivalent fractions. It is hard to tell by inspection whether or not the answer will be positive or negative, so don't guess, work it out to see.

The dimensions of a room are 10 feet by 10 feet. What is the area?

Correct answer: 100 ft^2 Explanation: Area implies to multiply lenght time width. Therefore 10feet x 10 feet= 100 ft^2 or 100 squared feet.

Fred drove 300 miles in 4 hours. How many miles can Fred drive in 2 days if he drives 8 hours per day?

Correct answer: 1200 Miles Explanation: Given: 300mi/4hr Fred drives 16 hours in two day. Therefore; 16hr x 300mi/4hr= units of hours cancel, 4 goes into 16, 4 times, and 4 times 300= 1200miles

Mary is 4 years older than Jane. If the combined sum of their ages is 32, how old is Jane?

Correct answer: 14 Explanation: (J+4) + J = 32 2J + 4 = 32 2J + 4 -4= 32-4 2J = 28, now divide both sides by 2, J = 14 and M=18 Jane is 14

Fred makes $12.34 per hour. John makes $10.98 per hour. After working for 8 hours, Fred makes time and a half for each additional hour worked. If John worked 10 hours, and Fred worked 10 hours, what would be the difference in pay, considering that Fred made 50% more an hour after working 8 hours?

Correct answer: 14.96 Explanation: John makes $10.98 for 10 hours with no extra for overtime. Multiply $10.98 times 10 hours for a total of $109.80. Fred makes $12.34 per hour for the first 8 hours, or $12.34 multiplied by 8 equalling $98.72. Fred then makes time and a half for the next 2 hours - $12.34 per hour multiplied by 1.5 equals $18.51 per hour times 2 hours for and total of $37.02 for the 2 extra hours. $37.02 plus the $98.72 Fred earned for his first 8 hours give Fred a total pay of $135.74. $135.74 minus $109.80 equals $25.94 more that Fred earned.

4 24/23 - 1 2/3 =

Correct answer: 3.38

Simplify, 23x ( 2x + 4) - 32x + 1.245y + 21x

Correct answer: 46x2 +81x +1.245y Explanation: There can be nothing done within the parentheses, so the next step is to muliply 23x times that which is in the paraenthesis. The next step is to see if any number can be factored out.

Mary made $28,990.87 for the year. She had to pay 20% of her salary to her husband for alimony. How much money did Mary have to pay monthly?

Correct answer: 483.18 Explanation: This question requires that you know how to use percentages. Simply take 20% of Mary's income, by multiplying her income time 0.20, then divide that number by 12 to find out how much she had to pay monthly.

Mark made twice as much as Fred. Fred made four times as much as Paul. If Mark made $400,000, how much did Paul make?

Correct answer: 50,000 Explanation: This problem requires that you know how to set up a question with a variable. We have three expressions: Mark made two times Fred or F/2 = M Fred made 4 times Paul or P/4 = F Mark made $400,000 Now substitute 400,000 for M and solve for F. Once you have solved for F, than solve for P.

(24x - 4) ( 2x - 2)8

Correct answer: 64 (6x-1) (x-1) Explanation: Factor out a 4 from one set of parentheses and and 2 from the other, this leaves 64 (6x-1)(x-1), in simpliest form

6/5 of 49 is similar to 7/8 of __________.

Correct answer: 67.2 Explanation: This is saying, 6/5 times 49 = 7/8 x multiply each side by 8/7, so "x" will be by itself, we have: 8/7(6/5)49 =x

There are 700 employees at the ACME firm. Out of 50% of the employees, only 57 will get bonuses. What is the percentages that won't get bonuses out of the total amount of employees?

Correct answer: 91.8% Explanation: It doesn't matter that only 57 employees out of 50% got bonuses. What does matter is that 700-57= the number of people that didn't get bonuses. Take that number and divide it into 700 to get the percentage.

Jake's salary after a five day work week is $550.00. If 10% of his salary is deducted for taxes weekly how much does he make per day?

Correct answer: 99 Explanation: Multiply 0.10 times 550.00 then divide by 5.

21x ( 3x +7) - 4x( 2.5x - 56x) + 24x/4

Correct answer: x ( 277x + 153) Explanation: Combine if you can all items in parentheses, then multiply, add and subtract.