Start by picking numbers for the variables in the problem. Since you will have to divide the dollar amounts by hours to calculate hourly wages, make the dollar values multiples of 10 and set the total hours equal to 10 to keep the division easy.

d = total pay = $100
t = cost of supplies = $20
y = total hours = 10
x = additional hours worked by Shawna = 2

Now, calculate the target values: the amount of money Shawna should give Jia to make their hourly wages equal.

The amount of money for total wages is equal to the total pay minus the supply costs:
$100 – $20 = $80

The hourly wage is the amount for wages divided by the total hours worked:
$80/10 = $8

Calculate the number of hours Jia worked. The two women worked a total of 10 hours and Shawna worked 2 more hours than Jia. Therefore, Shawna worked 6 hours and Jia worked 4 hours.

If Jia worked 4 hours and the hourly wage is $8, then she is owed $32 ($8 × 4).

$32 is your target value; this is the value you will get when you plug your smart numbers for the other variables into the correct answer.

Test Choice (A).

(d − t)(y + x)/2y=(100 − 20)(10 − 2)/2(10)=(80)(8)/20=4(8)=32

If you are short on time, you may choose to stop once you find a match for your target. Otherwise, test the remaining answers to ensure that no other answer matches the target.

Test Choice (B).

(d − t)/y=(100 − 20)/10=8


Test Choice (C).

(d − x)/y−t=((100 − 2)/10)−20≈−10


Test choice (D).

(dx − t)/2=(100(2) − 20)/2=90


Test choice (E).

(d − t)(y + x)/2y=(100 − 20)(10 + 2)/(2(10))=(80)(12)/20=48



Only choice (A) matches the target value