SSAT Upper Level Quantitative Quiz: Word Problems To Expressions

10 questions · exam conditions

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Word Problems To ExpressionsQuestion 1 of 10

A parking garage charges $3 for the first hour and $1.50 for each additional hour or fraction thereof. If someone parks for more than one hour, which expression correctly represents the total cost for parking $h $hours, where$ h > 1$?

3 + 1.5h

3 + 1.5(h - 1)

4.5h

3h + 1.5(h - 1)

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SSAT Upper Level Quantitative Quiz

SSAT Upper Level Quantitative Quiz: Word Problems To Expressions

Practice Word Problems To Expressions in SSAT Upper Level Quantitative with focused quiz questions that help you check what you know, review explanations, and build confidence with test-style prompts.

What this quiz covers

This quiz focuses on Word Problems To Expressions, giving you a quick way to practice the rules, question types, and explanations that matter most for SSAT Upper Level Quantitative.

How to use this quiz

Try each quiz question before looking at the correct answer. Use the explanations to review missed ideas, then come back to similar questions until the pattern feels familiar.

All questions

Question 1

$3 + 1.5h$
$3 + 1.5(h - 1)$ (correct answer)
$4.5h$
$3h + 1.5(h - 1)$

Explanation: For

h

hours where

h > 1

, you pay $3 for the first hour and $1.50 for each of the remaining $(h-1)

hours. This gives

3 + 1.5(h-1)

. Choice A incorrectly charges $1.50 for all $h

hours instead of just the additional hours. Choice C uses a flat rate per hour, ignoring the different first-hour rate. Choice D incorrectly adds both a rate of $3 per hour for all hours plus the additional hour charge.

Question 2

In a basketball league, teams earn 3 points for a win, 1 point for a tie, and 0 points for a loss. If a team has played $g$ games and has $w$ wins and $t$ ties, which expression represents the number of losses?

$g - w - t$ (correct answer)
$g - w + t$
$w + t - g$
$g - (w + t)$

Explanation: The total games played equals wins plus ties plus losses, so

g = w + t + \text{losses}

. Solving for losses:

\text{losses} = g - w - t

. Choice B incorrectly adds ties instead of subtracting. Choice C would give a negative result in most realistic scenarios. Choice D is mathematically equivalent to choice A, but choice A is the more direct representation.

Question 3

A movie theater has rows of seats where the first row has $f$ seats, and each subsequent row has 2 more seats than the previous row. Which expression represents the total number of seats in the first $n$ rows?

$f + 2n$
$nf + 2n(n-1)$
$nf + n(n-1)$ (correct answer)
$f + 2(n-1)$

Explanation: The rows have

f

f+2

f+4

, ...,

f+2(n-1)

seats. This is an arithmetic sequence with first term

f

, common difference 2, and

n

terms. The sum is

nf + \frac{n(n-1)}{2} \cdot 2 = nf + n(n-1)

. Choice A gives seats in just the

n

th row, not the total. Choice B doubles the additional seats incorrectly. Choice D also gives seats in just one row.

Question 4

A car rental company charges a base fee plus a mileage charge. The total cost for renting a car for one day and driving $m$ miles is $C = 45 + 0.25m$ dollars. If a customer's total bill was $78.50, which equation could be used to find the number of miles driven?

$45 + 0.25m = 78.50$ (correct answer)
$45m + 0.25 = 78.50$
$0.25m - 45 = 78.50$
$45 + 0.25 = 78.50m$

Explanation: Given the cost formula

C = 45 + 0.25m

and total bill of $78.50, we substitute to get

45 + 0.25m = 78.50

. Choice B incorrectly makes the base fee coefficient of

m

. Choice C incorrectly subtracts the base fee instead of adding it. Choice D incorrectly makes the total cost a coefficient rather than the result.

Question 5

A bookstore offers a membership plan where customers pay an annual fee of $25 and then receive a 15% discount on all purchases. If a member buys books worth $d$ dollars (before discount) during the year, which expression represents the total amount the member pays for the year including the membership fee?

$25 + 0.15d$
$25 + 0.85d$ (correct answer)
$25 + d - 0.15d$
$40 + 0.85d$

Explanation: The member pays $25 for the annual fee plus the discounted price of books. With a 15% discount, the member pays 85% of the original price, which is

0.85d

. So the total is

25 + 0.85d

. Choice A incorrectly adds the discount amount instead of subtracting it. Choice C is mathematically equivalent to the correct answer but unnecessarily complicated. Choice D uses an incorrect membership fee.

Question 6

A school cafeteria sells lunch combinations where students choose one item from each category. There are $s$ sandwich options, $d$ drink options, and $c$ chips options. If the cafeteria removes 2 sandwich options but adds 3 new drink options, which expression represents the new total number of possible lunch combinations?

$(s - 2)(d + 3)c$ (correct answer)
$(s - 2) + (d + 3) + c$
$s - 2 + d + 3 + c$
$sdc - 2 + 3$

Explanation: The number of combinations is the product of choices in each category. After changes:

(s-2)

sandwich options,

(d+3)

drink options, and

c

chips options. Total combinations =

(s-2)(d+3)c

. Choice B incorrectly adds instead of multiplying the categories. Choice C fails to group the changes properly and adds instead of multiplies. Choice D incorrectly modifies the original product by simple addition/subtraction.

Question 7

At a farmer's market, apples cost $2.50 per pound and oranges cost $3.20 per pound. A customer buys $a$ pounds of apples and $o$ pounds of oranges, then uses a coupon for $1.75 off the total purchase. Which expression represents the amount the customer actually pays?

$2.50a + 3.20o - 1.75$ (correct answer)
$(2.50a - 1.75) + 3.20o$
$2.50(a - 1.75) + 3.20o$
$2.50a + 3.20o + 1.75$

Explanation: The total before coupon is

2.50a + 3.20o

. After applying the $1.75 coupon, the amount paid is

2.50a + 3.20o - 1.75

. Choice B incorrectly applies the coupon only to apples. Choice C incorrectly reduces the pounds of apples by the coupon amount. Choice D incorrectly adds the coupon instead of subtracting it.

Question 8

A company produces widgets at a cost of $3.50 each, plus a daily fixed cost of $200 for equipment. If the company sells each widget for $7.25 and produces and sells $x$ widgets in a day, which expression represents the daily profit?

$7.25x - (3.50x - 200)$
$7.25x - 3.50x + 200$
$7.25x - 200$
$7.25x - 3.50x - 200$ (correct answer)

Explanation: When you encounter profit problems, remember that profit equals revenue minus all costs. You need to carefully identify each component and how they behave. Let's build the profit expression step by step. Revenue from selling

x

widgets at $7.25 each is

7.25x

. Total costs have two parts: variable costs that depend on production quantity ($3.50 per widget, so

3.50x

total) and fixed costs that remain constant regardless of quantity ($200 daily equipment cost). Therefore, total costs are

3.50x + 200

. Daily profit = Revenue - Total Costs =

7.25x - (3.50x + 200) = 7.25x - 3.50x - 200

This matches answer choice D. Let's examine why the other options are incorrect: Choice A:

7.25x - (3.50x - 200)

incorrectly subtracts the fixed cost from variable costs instead of adding them together. This would give you

7.25x - 3.50x + 200

, which unrealistically adds the fixed cost to profit. Choice B:

7.25x - 3.50x + 200

makes the same error as A's simplified form—it treats the fixed cost as contributing to profit rather than reducing it. Choice C:

7.25x - 200

completely ignores the variable production costs of $3.50 per widget, severely overestimating profit. Strategy tip: In profit problems, always write out "Profit = Revenue - Total Costs" first, then carefully identify all cost components. Fixed costs always reduce profit, while variable costs multiply by the quantity produced.

Question 9

A rectangular garden has length that is 8 feet more than twice its width. If the width is $w$ feet, and the gardener wants to install a fence around the entire perimeter plus an additional gate that costs the same as 5 feet of fencing, which expression represents the total feet of fencing needed?

$2w + (2w + 8) + 5$
$w(2w + 8) + 5$
$2w + 2(2w + 8) + 5$ (correct answer)
$2w + 2(2w + 8)$

Explanation: This problem tests your understanding of perimeter formulas and algebraic expressions. When you see a geometry problem involving perimeter plus additional costs, break it down into separate components. First, identify the dimensions. The width is

w

feet, and the length is "8 feet more than twice the width," which translates to

2w + 8

feet. The perimeter of any rectangle equals

2 \times \text{length} + 2 \times \text{width}

, so you need

2(2w + 8) + 2w

feet of fencing for the perimeter. Additionally, the gate costs the same as 5 feet of fencing, so you add 5 to the total. The complete expression is

2(2w + 8) + 2w + 5

, which can be written as

2w + 2(2w + 8) + 5

. Looking at the wrong answers: Choice A gives

2w + (2w + 8) + 5

, which only accounts for one width and one length instead of the full perimeter—this would be half the perimeter plus the gate cost. Choice B shows

w(2w + 8) + 5

, which calculates the area of the rectangle (length times width) rather than the perimeter. Choice D gives

2w + 2(2w + 8)

but forgets to include the additional 5 feet for the gate cost. Remember that perimeter problems require you to go around the entire shape, so you need two lengths and two widths. Always read carefully to catch additional costs beyond the basic perimeter calculation—these are common on the SSAT.

Question 10

A subscription service offers two plans: Plan A costs $12 per month, and Plan B costs $8 per month plus $0.50 for each hour of usage. After how many hours of usage in a month would Plan B cost the same as Plan A?

$8 + 0.50h = 12h$
$8h + 0.50 = 12$
$12h = 8 + 0.50h$
$8 + 0.50h = 12$ (correct answer)

Explanation: When you encounter a word problem asking when two costs will be equal, you need to set up an equation where both expressions represent the same total cost. Plan A has a simple structure: $12 per month regardless of usage. Plan B has two components: a base fee of $8 plus $0.50 multiplied by the number of hours used. If we call the hours $

h

, then Plan B costs

8 + 0.50h

$ dollars. To find when the plans cost the same, you set them equal: the fixed cost of Plan A (

) equals the variable cost of Plan B (

8 + 0.50h

). This gives you the equation

8 + 0.50h = 12

. Looking at the wrong answers: Choice A incorrectly makes Plan A's cost

12h

, as if the $12 were multiplied by hours instead of being a flat monthly fee. Choice B switches the roles of the base fee and hourly rate in Plan B, writing

8h + 0.50

instead of

8 + 0.50h

. Choice C makes the same error as choice A by writing Plan A as

12h

, and also incorrectly structures the equation. The key strategy for cost comparison problems is to carefully identify what stays constant versus what varies. Write out each plan's total cost formula first, then set them equal. Watch out for mixing up which numbers get multiplied by the variable—flat fees stay as constants, while per-unit charges get multiplied by the usage amount.