First, find the ages of Maria and Sam: Maria is y, Sam is y - 4. The sum of their ages is \(y + (y - 4) = 2y - 4\). Twice the sum of their ages is \(2(2y - 4) = 4y - 8\). The father is 1 year more than this, so his age is \((4y - 8) + 1 = 4y - 7\).

The average is the total sum of scores divided by the number of tests. The sum of the scores for the first n tests is 88n. After scoring 96 on the next test, the new total sum is 88n + 96. The new number of tests is n + 1. Therefore, the new average is the new sum divided by the new number of tests: \(\frac{88n + 96}{n + 1}\).

A fence of length L with posts every f feet is divided into L/f sections. For example, a 24-foot fence with posts every 8 feet has 3 sections. The number of posts needed is one more than the number of sections, because there is a post at the start of each section plus one final post at the very end. Therefore, the number of posts is \(\frac{L}{f} + 1\).

If k is the smallest of three consecutive even integers, the next even integer is k + 2, and the one after that is k + 4. The sum of these three integers is \(k + (k + 2) + (k + 4)\). Combining like terms gives \(3k + 6\).

Profit is calculated as (Revenue - Cost). A more direct way is to find the profit per item and multiply by the number of items sold. The profit on one cupcake is \((3-c)\). The profit on one cookie is \((2-k)\). For 70 cupcakes, the profit is \(70(3-c)\). For 120 cookies, the profit is \(120(2-k)\). The total profit is the sum of the profit from cupcakes and cookies: \(70(3-c) + 120(2-k)\).

The student's score is based on the points gained from correct answers minus the points lost from incorrect answers. The points gained are 5c. The points lost are 2i. The total score is \(5c - 2i\). The total number of questions (40) is extra information not needed to write the expression for the score, as the number of unanswered questions does not affect the score.

First, express the number of each coin in terms of d. Number of dimes = d. Number of quarters = 2d + 3. Next, find the value of each set of coins in cents. Value of dimes = 10d. Value of quarters = \(25(2d + 3) = 50d + 75\). The total value is the sum: \(10d + 50d + 75 = 60d + 75\).

First, calculate the discounted price. A 30% discount means the price is 70% of the original, so the discounted price is 0.70p. Next, calculate the 7% sales tax on this new price. An increase of 7% is equivalent to multiplying by 1.07. So, the final cost is \(1.07 \times(0.70p)\). Choice D is equivalent, but the order in A better reflects the sequence of operations described.

This question tests middle school quantitative reasoning skills by translating situations into algebraic expressions. The core concept involves understanding how real-world quantitative data can be represented using variables and operations in mathematics. In this specific stimulus, the class sells s bracelets at $4 each, requiring us to find the total earnings from this fundraiser. Choice C is correct because it accurately models the situation by multiplying the number of bracelets sold (s) by the price per bracelet ($4), giving 4s. Choice A is incorrect because it adds 4 to s instead of multiplying, which would only increase the count by 4 rather than calculating total revenue. To help students, encourage practice in identifying key quantitative relationships and expressing them algebraically. Teach them to recognize when multiplication is needed (for repeated addition or rate problems) versus when simple addition or subtraction applies.

This question tests middle school quantitative reasoning skills by translating situations into algebraic expressions. The core concept involves understanding how real-world quantitative data can be represented using variables and operations in mathematics. In this specific stimulus, Jordan starts with j dollars and makes two purchases: a game for $15 and a snack for $3, requiring us to find the remaining balance. Choice A is correct because it accurately models the situation by subtracting the total cost of both items (15+3 = $18) from the initial amount j, giving j-(15+3). Choice B is incorrect because it subtracts only the game cost first, then adds 3, which would increase rather than decrease the balance after the second purchase. To help students, encourage practice in identifying key quantitative relationships and expressing them algebraically. Teach them to group multiple expenses together before subtracting from the initial amount, and watch for the importance of proper parentheses usage.