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 5

Question 12345 of 5

Question 1 of 5

A school is selling tickets to a play. Student tickets cost \6\ each. On the first night, 120 tickets were sold for a total of \920

Explanation Let s be the number of student tickets and a be the number of adult tickets. The total number of tickets gives s + a = 120. The total revenue gives 6 s + 10 a = 920. Substitute s = 120 - a into the revenue equation: 6 (120 - a) + 10 a = 920. Simplify: 720 - 6 a + 10 a = 920 720 + 4 a = 920 4 a = 200 a = 50. So, 50 adult tickets were sold. Concept summary Use a system of equations when two quantities are connected by both a total amount and a total value. Define variables, write one equation for the count and one for the cost, then solve.

Question 2 of 5

A delivery company charges a fee based on the distance of each trip. The table shows two points on the graph of total cost versus miles traveled for the company: Miles traveled 410 Total cost (dollars) 1833 If the relationship is linear, which expression gives the total cost, in dollars, for a trip of m miles?

Explanation Because the relationship is linear, find the slope using the two data points: \frac{33 - 18}{10 - 4} = \frac{15}{6} = 2.5. So the cost model has the form C = 2.5 m + b . Substitute the point (4, 18) : 18 = 2.5 (4) + b = 10 + b, so b = 8. Therefore the expression for total cost is 2.5 m + 8. Concept summary For a linear model from a table, find the slope from the changes in the two columns, then use one data point to determine the y-intercept in the expression y = m x + b .

Question 3 of 5

At a school fundraiser, the total amount collected came from selling adult tickets for \12\ each. The number of student tickets sold was more than twice the number of adult tickets sold. If the fundraiser collected \456

Explanation Let a be the number of adult tickets sold. Then the number of student tickets sold was 2 a + 15 . The total revenue equation is 12 a + 8 (2 a + 15) = 456. Simplify: 12 a + 16 a + 120 = 456 28 a + 120 = 456 28 a = 336 a = 12. So, 12 adult tickets were sold. Concept summary Model each quantity with a variable expression, write an equation for the total, and solve. In word problems, both the relationship between quantities and the units in the total matter.

Question 4 of 5

For two numbers, the larger number is 7 more than twice the smaller number. If their sum is 52, what is the smaller number?

Explanation Let the smaller number be x . Then the larger number is 2 x + 7 . Since their sum is 52, x + (2 x + 7) = 52 So, 3 x + 7 = 52 3 x = 45 x = 15 Therefore, the smaller number is 15 . Concept summary Translate each quantity into an algebraic expression, write an equation from the given constraint, and solve for the unknown.

Question 5 of 5

On the coordinate plane, a line passes through the point (4, 10) and has a y -intercept of 2 . Which expression is equivalent to the equation of this line?

Explanation A line with y -intercept 2 has the form y = m x + 2 . Since the line passes through (4, 10), substitute these values: 10 = 4 m + 2 . Then 8 = 4 m, so m = 2 . The equation is y = 2 x + 2, which is equivalent to the line described. Concept summary To write an equivalent form of a line from a point and an intercept, use slope-intercept form y = m x + b, identify b, then solve for m with the given point.

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.

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Your results

2of 5 correct

Estimated SAT Math band

600-650

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

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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.

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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.

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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 is selling tickets to a play. Student tickets cost \ 6 e a c h , an d a d u l tt i c k e t scos t \ 10 each. On the first night, 120 tickets were sold for a total of \ 920 . H o w man y a d u l tt i c k e t s w er eso l d ?

Q2. A delivery company charges a fee based on the distance of each trip. The table shows two points on the graph of total cost versus miles traveled for the company: Miles traveled 4 10  Total cost (dollars) 18 33   If the relationship is linear, which expression gives the total cost, in dollars, for a trip of m miles?

Q3. At a school fundraiser, the total amount collected came from selling adult tickets for \ 12 e a c han d s t u d e n tt i c k e t s f or \ 8 each. The number of student tickets sold was 15 more than twice the number of adult tickets sold. If the fundraiser collected \ 456 f r o m t i c k e t s a l es , h o w man y a d u l tt i c k e t s w er eso l d ?

Q4. For two numbers, the larger number is 7 more than twice the smaller number. If their sum is 52 , what is the smaller number?

Q5. On the coordinate plane, a line passes through the point ( 4 , 10 ) and has a y -intercept of 2 . Which expression is equivalent to the equation of this line?