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Algebra · Word Problems Involving Algebraic Expressions

SAT Word Problems Involving Algebraic Expressions Practice Questions (Free + Explanations) | Quiz 8

Question 12345 of 5

Question 1 of 5

A theater charges a base rental fee of dollars plus dollars for each ticket sold. For one event, the total amount collected was dollars, and the base rental fee was of that total. Which expression is equivalent to the number of tickets sold for that event?

Explanation

The total amount collected can be written as base fee plus ticket revenue:

where is the number of tickets sold.

The statement that the base rental fee was of the total means

but the question asks for an expression equivalent to the number of tickets sold, so solve the total-revenue equation for :

So the equivalent expression is .

Concept summary

Translate the word problem into an equation for total amount, then isolate the quantity being asked for. A statement about a percent of the total can describe a variable, but the correct equivalent expression must still match the requested form.

Question 2 of 5

A concert venue sells tickets in two stages. In the first stage, adult tickets cost \18\ each. All tickets available for the concert were sold in this stage, for a total of \4{,}56020

Explanation

Let be the number of adult tickets and be the number of student tickets sold at first. Then

and

Substitute into the revenue equation:

So adult tickets and student tickets were originally sold.

Each of the customers who exchanged an adult ticket for a student ticket received a refund of

dollars. The total refund was

dollars.

Therefore, the venue's final revenue was

Concept summary

Model the situation with equations to find original quantities, then adjust the original total by the net change caused by the exchange.

Question 3 of 5

A concert venue charges a one-time facility fee plus a fixed price per ticket for online orders. For an order of 3 tickets, the total cost is . For an order of 5 tickets, the total cost is . What is the total cost, in dollars, of an online order of 4 tickets?

Explanation

Let be the one-time facility fee and let be the price per ticket. Then the two orders give the system

Subtract the first equation from the second:

so . Substitute into :

so . For 4 tickets, the total cost is

So the total cost is dollars.

Concept summary

Model a word problem with a fixed fee and a per-item rate using linear expressions, then use the given totals to find the missing cost.

Question 4 of 5

A theater charges the same ticket price for every student ticket. Last Friday, the theater sold student tickets and collected a total of dollars. This Friday, it sold more student tickets than last Friday and collected more dollars than last Friday. Which equation can be used to find the price, in dollars, of one student ticket?

Explanation

Let be the price of one student ticket. Last Friday, tickets brought in dollars, so the total was . This Friday, the theater sold tickets and collected dollars. Therefore, the equation that models this Friday's sales is .

Concept summary

Translate the situation carefully: update both the ticket count and the total revenue, then write an equation using price number of tickets total revenue.

Question 5 of 5

A gym charges a one-time membership fee of dollars and a monthly fee of dollars. After 6 months, the total amount paid is represented by . Which expression represents the total amount paid after 10 months in terms of and the amount paid after 6 months?

Explanation

The expression includes the one-time membership fee and 6 monthly payments of . After 10 months, the total is . Since is already the amount after 6 months, add 4 more monthly fees:

So the equivalent expression is .

Concept summary

When rewriting a word-problem expression in an equivalent form, identify what part of the total is already included and then add only the extra amount needed.

Your results

0of 5 correct

Estimated SAT Math band

500-550

Illustrative range from this short quiz—not an official College Board score.

Adaptive practice, weak-area review, and timed tests live in the MCQsLearn app—pick up where you left off on your phone.

More SAT Math practice

Your results

1of 5 correct

Estimated SAT Math band

500-550

Illustrative range from this short quiz—not an official College Board score.

Adaptive practice, weak-area review, and timed tests live in the MCQsLearn app—pick up where you left off on your phone.

More SAT Math practice

Your results

2of 5 correct

Estimated SAT Math band

600-650

Illustrative range from this short quiz—not an official College Board score.

Adaptive practice, weak-area review, and timed tests live in the MCQsLearn app—pick up where you left off on your phone.

More SAT Math practice

Your results

3of 5 correct

Estimated SAT Math band

600-650

Illustrative range from this short quiz—not an official College Board score.

Adaptive practice, weak-area review, and timed tests live in the MCQsLearn app—pick up where you left off on your phone.

More SAT Math practice

Your results

4of 5 correct

Estimated SAT Math band

700+

Illustrative range from this short quiz—not an official College Board score.

Adaptive practice, weak-area review, and timed tests live in the MCQsLearn app—pick up where you left off on your phone.

More SAT Math practice

Your results

5of 5 correct

Estimated SAT Math band

700+

Illustrative range from this short quiz—not an official College Board score.

Adaptive practice, weak-area review, and timed tests live in the MCQsLearn app—pick up where you left off on your phone.

More SAT Math practice