Quantitative reasoning 4 DAT REVIEW

a man bought 8 books at an average price of $6.00 and 10 books at an average price of $2.40. find the average cost of the books.

$4.00 average cost per book= total cost/totalbooks= 8(6)+10(2.4)/8+10= 48+24/18= 72/18=4

x+y+3z=7;3x+6y+6z=8 what is the numerical value of (y-z)

-13/3 first we want to remove x so we multiply the first equation by 3 and subtract it from the second equation 3x+6y+6z=8 -3x+3y+9z=21 3y=3z=-13 3(y-z)=-13 y-z= -13/3

what is the value of y if 3x-2y=9 and 7x+y=4?

-3 we need to solve these equations simultaneously so we need to get one variable out so 3x and 7x share a common variable which is 21 so we can convert both equations to 21X so the first equation I will multiply everything by 7 to get: 21x-14y=63 and then I will multiply the second equation by 3 to get: 21X+3y=12 if we subtract the second equation from the first we will get: -17y=51 solving for y we get -3

when the expression square root of 1+9/16 is simplified, which of the following is obtained?

1 1/4 1+9/16= 16/16+9/16= 25/16 square root of 1+9/16= square toot of 25/16 = 5/4 = 1 1/4

A,B and C have 24 marbles between them. A has more marbles than B and B has more marbles than C. what is the largest number of marbles that B can have?

11 B will have a max number of marbles when the others (A and C) have their min number according to the constraints. Since C has less than both A and B his min is zero. Therefore, A and B have 24 together. If A is to have more than B and B is to have max, A will have 13 and B will have 11

anne has a total of $34 in nickels, dimes, and quarters. if she has 3 times as many dimes as quarters and 2 times as many nickels as dimes, how many dimes does she have?

120 $34=(n)(1/20) + (d)(1/10) + (q)(1/4) $34= (2d)(1/20) + (d)(1/10) + (d/3)(1/4) $34= d/10 + d/10 + d/12 = 2d/10 + d/12= 24d/120 + 10d/120= $34= 34d/120 d=120

a rectangular swimming pool that measures 24 ft by 16 ft is filled to a height of 1 ft. how high would the same mat of water reach in a 20ft by 8 ft pool

2 2/5ft (length)(width)(height) let h = the height the water would reach in the second pool (24 feet)(16feet)(1foot)=(20feet)(8feet)(hft) this can be rearranged to : (24ft^2)(16ft)=(160ft^2)(hft) 2(12ft^2)(16ft)=2(5ft)(hft)(16ft) after cancelling like factors: 12ft^2=5hft^2; h= 2 2/5ft

the ratio of juniors to non juniors at a college is 7:20 and there are a total of 810 students at the college. how many juniors are there?

210 the ratio of 7 to 20 tells us that for every 7 juniors, there are 20 non juniors. it also tells us that there are a total of 7+20=27 equal parts. these 27 equal parts make up the total of 810 students. so each of these equal parts is 810/27= 30 students the juniors consists of 7 of these equal parts, so there are 7 x 30= 210 juniors

15 is 6% of what number?

250 6%of x= 15 x=15/6=2.5 x 100= 250

a motorist travels 50 miles at 20mph. he returns the same distance at 50mph. what is the average rate for the entire trip?

28 4/7 average rate= total distance/total time the trip going takes 2.5 hours. the trip returning takes 1 hour. total time= 3.5 hours= 7/2 hours average rate= 50+50/(7/2) = 200/7= 28 4/7mph

solve for x in the equation 32-10squareroot 5X/3=4

4/5 multiply both sides by 3 32-10 square root 5x= 12 add and subtract to isolate 20=10 square root 5x divide by 10 2= 5x square both side 4=5x x=4/5

what is the approx length in feet, of a ladder whose base is 45 ft from the foot of a building and reaches up 24 ft along the wall of a building?

51 notice this is the pythagorean triple 8:15:17, with each leg multiplied by 3. the length of the hypotenuse(ladder) is then 17x3-51ft

what is the length of side AB in equilateral triangle ABC if the length of altitude AD is 12?

8 square root 3 we are given that ABC is equilateral, which means that each leg of the triangle is equal. the altitude of an equilateral triangle bisects to the base, so BD=CD= 1/2AB .. (1/2)^2+12^2=x^2

the length of a rectangle is twice the width. if the perimeter of a square equals the perimeter of the rectangle, what is the ratio of the area of the rectangle to the area of the square?

8:9 let the width be 10(for the rectangle). Therefore, the length is 20 and the perimeter is 2(10+20)=60 The perimeter of the square is also 60 which gives a side of 15. the area of the rectangle is (10)(20)=200 the area of the square is (15)(15)=225 the ratio= 200:225= 40:45= 8:9

the numerator of a fraction is doubled and the denominator is halved. the value of the fraction is

multiplied by 4 when the numerator is doubled, the value of the fraction is doubled. when the denominator is halved, the value of the fraction is again doubled. the net result is quadrupling (multiplying by 4)

what is equal to -x-2/(2-x)(3-x)

x-2/(2-x)(3-x)

the point (-14,12) is a point on line l. Line l is perpendicular to the line with the equation y=7/2x-3/4. which is an equation of line l?

y=-2/7x+8 the slope will be the negative reciprocal of 7/2 so -2/7 and then solve for b by plugging in the x and y points

line l is perpendicular to the line with the equation y= -1/5x, and the point (3,-10) is on line l. which of the following is an equation of line l?

y=5x-25 y=mx+b y=5x+b -10=5(3)+b -10=15+b -10-15=b -25=b now we know that m= 5 and b = -25