How to find the whole from the part

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SAT Math › How to find the whole from the part

Questions 1 - 5

A pitcher of water is filled $\dpi{100} \small \frac{2}{5}$ of full. An additional 27 ounces of water is added. Now the pitcher of water is completely full. How much water does the pitcher hold?

Explanation

If $\dpi{100} \small 27$ ounces fills the pitcher, then it must equal the volume of $\dpi{100} \small \frac{3}{5}$ of the pitcher. If $\dpi{100} \small \frac{3}{5}$ of a pitcher equals 27 ounces, then $\dpi{100} \small \frac{1}{5}$ of a pitcher equals $\dpi{100} \small 27\div 3=9$ ounces. Since there are $\dpi{100} \small 5$ fifths in the pitcher, it must hold $\dpi{100} \small 9\times 5=45$ ounces total.

If Mr. Jones’ math class has 8 boys and two-thirds of the class are girls, how many total students are in the class?

Explanation

If two-thirds of the class are girls, then one-third must be boys. Set up an equation comparing the number of boys to how much they represent in the entire class:

8 = (1/3) x, where x is the number in the entire class.

When we solve for x in the equation we get x = 24.

Mr. Owens spent $7.50 for a dinner buffet. The amount he paid accounted for 3/4 of the money in his wallet. How much money is left in his wallet for other expenses?

$10.00

$6.50

$4.00

$2.50

$1.00

Explanation

If $7.50 is 3/4 of the total, 7.50/3 gives us what 1/4 of his total money would be. This equals $2.50, the remaining unspent quarter.

is what of what?

Explanation

With the given information, we can set up a proportion.

$\frac{6}{x}=\frac{30}{100}$

A certain ball that is dropped will bounce back to 3/5 of the height it was initially dropped from. If after the 2nd bounce the ball reaches 39.96 ft, what was the initial height the ball was dropped from?

150 ft

111 ft

135 ft

100 ft

66 ft

Explanation

We know the height of the initial bounce, so work backwards to find the initial height. 39.96/0.6 = 66.6 = height of ball after first bounce

66.6/0.6 = 111 ft

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