Melissa had 3 fewer apples than Marcia. Then, she gave 2 apples to Marcia. Now how many fewer apples does Melissa have than Marcia?

Solution
To solve this problem, it is useful to assign values to the number of apples that Melissa and Marcia both possess.
If Marcia has 10 apples, Melissa has 10 − 3 = 7 apples.
If Melissa gives 2 of her 7 apples to Marcia, Melissa is left with 7−2 = 5 apples.
When Marcia receives 2 more apples, she has 10 + 2 = 12 apples.
Since Marcia now has 12 apples and Melissa now has 5 apples, Melissa has 12−5 = 7 fewer apples than Marcia.
Andrew won a cash prize on a game show. Andrew paid taxes of 30% on the original cash prize and had $28,000 remaining. How much was the original cash prize?

Solution
In order to solve this problem, you must realize that if Andrew had $28,000 remaining after paying 30% in taxes, then the $28,000 constitutes 100%−30% or 70% of the original prize, P.
Therefore, 0.7P = 28,000.
Dividing by 0.7, you can conclude that the original cash value of the prize was P = \(\frac{28,000}{0.7}\) ,or $40,000.
What is the slope of any line parallel to the line 2x − 3y = 7?

Solution
A carton of paper is priced at $27.00 now. If the paper goes on sale for 25% off the current price, what will be the sale price of the carton?

Solution
The easiest way to solve this problem is to take 25% of the original price and deduct it from the original price.
To find 25% of the sale price of the carton of paper, you would multiply $27.00 by 25%, or 0.25.
Therefore, the sale price of the carton of paper would be $27.00 − ($27.00)(0.25) = $27.00 − $6.75, or $20.25.
In the figure showing ΔPQR below, line l is parallel to line m. Which one of the following angles must be congruent to ∠y?

Solution
When parallel lines are cut by a transversal (such as segment PR in this problem), “alternate interior angles” are congruent.
In this problem, ∠y and ∠4 are alternate interior angles, and so you can conclude that they are congruent.
The daily totals of enrollments at Sunnyside Summer Camp last Monday through Saturday were 17, 19, 23, 14, 25, and 28. What was the average number of enrollments per day?

Solution
Unless otherwise specified, average means “arithmetic mean,” which is defined as the sum of a set of values divided by the number of values.
Therefore, you can see that the average number of enrollments per day is \(\frac{(17 + 19 + 23 + 14 + 25 + 28)}{6}=\frac{126}{6}\), or 21.
Seth has 4 plaid shirts and 5 solidcolored shirts hanging together in a closet. In his haste to get ready for work, he randomly grabs 1 of these 9 shirts. What is the probability that the shirt Seth grabs is plaid?

Solution
Because Seth has 4 plaid shirts and 5 solidcolored shirts, the total number of shirts is 4+5 = 9. Of these 9 shirts, 4 are plaid.
Thus the probability that a randomly selected shirt will be plaid is ^{4}⁄_{9}.
A distance in meters, M, can be approximated by multiplying a distance in yards, Y, by 1.0936. Which of the following expresses this approximation method? (Note: The symbol ≈ means “is approximately equal to.”)

Solution
Since a distance in meters, M, can be approximated by multiplying a distance in yards, Y, by 1.0936, it follows that M ≈ Y(1.0936).
Given right triangle ΔMNO below, how many units long is \(\overline{NO}\)?

Solution
To solve, use the Pythagorean Theorem (c^{2} = a^{2}+b^{2}). Using values from MNO, you can set up the equation like this:
10^{2} = 6^{2} + NO^{2}
100 = 36 + NO^{2}
NO^{2} = 100 − 36 = 64
NO = ^{2} = 8
In the standard (x,y) coordinate plane, point X has coordinates (−4,0) and point Y has coordinates (0,−8). What are the coordinates of the midpoint of \(\overline{XY}\)?

Solution
To find the midpoint of two points, you can take the average of the x and y coordinates. If point X has coordinates (−4,0) and point Y has coordinates (0,−8), then the midpoint is:
\(\left ( \frac{(−4 + 0)}{2},\frac{(0 + −8)}{2} \right )\)
\(\left ( \frac{4}{2},\frac{8}{2} \right )\)
(−2, −4)