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

Algebra · Word Problems Involving Algebraic Expressions

SAT Word Problems Involving Algebraic Expressions Practice Questions (Free + Explanations) | Quiz 2

Question 12345 of 5

Question 1 of 5

A school store tracks the number of notebooks sold and the total money collected, as shown in the table. Notebooks sold 4710 Total money collected (dollars) 10 17.50 25 If this pattern continues, which expression gives the total money collected, in dollars, for selling n notebooks?

Explanation From the table, each notebook costs the same amount. Using any row, divide total money by number sold: 10 \div 4 = 2.5, 17.50 \div 7 = 2.5, and 25 \div 10 = 2.5 . So the total money for n notebooks is 2.50 times n, which is 2.50 n . Concept summary In a table with a constant rate, find the unit price and multiply it by the number of items to write the expression.

Question 2 of 5

A gym charges a one-time sign-up fee of s dollars and a monthly fee of 25 . The total cost for 4 months is 140 . Which statement must be true?

Explanation The total cost is the sign-up fee plus 4 monthly payments of 25 . So, s + 4 (25) = 140 Since 4 (25) = 100, we get s + 100 = 140 Subtracting 100 from both sides gives s = 40 So the statement that must be true is s = 40 . Concept summary Translate the situation into an expression: total cost = one-time fee + monthly fee times number of months.

Question 3 of 5

A rectangular garden has a length of 12 feet and a width of w feet. If the area of the garden is 84 square feet, what is the value of w ?

Explanation Use the area formula for a rectangle: area = length \times width . So 84 = 12 w . Dividing both sides by 12 gives w = 7. Concept summary For a rectangle, area equals length times width. If the area and one side are known, divide to find the missing side.

Question 4 of 5

A ride-sharing company charges a base fee represented by the y -intercept of a line. The total cost y, in dollars, for a trip of x miles is modeled by a line with slope 2 that passes through the point (3, 11) . What is the base fee?

Explanation The slope is 2, so the cost increases by 2 dollars per mile. A line with slope 2 that passes through (3, 11) has equation y = 2 x + b . Substitute x = 3 and y = 11 : 11 = 2 (3) + b = 6 + b . So b = 5 . The y -intercept, which represents the base fee, is 5 . Concept summary For a line written as y = m x + b, the slope is m and the y -intercept is b . Use a known point to solve for b .

Question 5 of 5

A school theater charges a flat equipment fee of 12 plus 3 dollars for each spotlight it rents. If the total cost is 27 dollars, how many spotlights were rented?

Explanation Let s be the number of spotlights. The total cost is modeled by 12 + 3 s = 27 . Subtract 12 from both sides to get 3 s = 15, and then divide by 3 to get s = 5 . So 5 spotlights were rented. Concept summary Write a verbal situation as an equation with a fixed amount plus a rate, then solve for the variable.

Your results

0of 5 correct

Estimated SAT Math band

500-550

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

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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.

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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.

Download on the App Store Get it on Google Play

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.

Download on the App Store Get it on Google Play

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.

Download on the App Store Get it on Google Play

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.

Download on the App Store Get it on Google Play

More SAT Math practice

Practice outline (enable JavaScript for interactive mode)

Q1. A school store tracks the number of notebooks sold and the total money collected, as shown in the table. Notebooks sold 4 7 10  Total money collected (dollars) 10 17.50 25   If this pattern continues, which expression gives the total money collected, in dollars, for selling n notebooks?

Q2. A gym charges a one-time sign-up fee of s dollars and a monthly fee of 25 . The total cost for 4 months is 140 . Which statement must be true?

Q3. A rectangular garden has a length of 12 feet and a width of w feet. If the area of the garden is 84 square feet, what is the value of w ?

Q4. A ride-sharing company charges a base fee represented by the y -intercept of a line. The total cost y , in dollars, for a trip of x miles is modeled by a line with slope 2 that passes through the point ( 3 , 11 ) . What is the base fee?

Q5. A school theater charges a flat equipment fee of 12 plus 3 dollars for each spotlight it rents. If the total cost is 27 dollars, how many spotlights were rented?