SAT Linear Modeling / Word Problems

Linear modelling word problems ask you to build an equation from a described situation: a fixed amount plus a rate times a quantity. The work is translation — deciding which number is the constant and which is the per-unit rate.

Practise this skill freeHow the SAT is structured
MathAlgebra124 questions
The trap on this skill

Dividing the fixed fee by the higher rate instead of by the difference between the rates.

How this skill behaves

What 124 questions on it look like

90% of these questions can appear in the harder second module. On a section-adaptive test that matters: this is a skill that keeps mattering after a strong first module, not one you leave behind.

Not one question in this skill is rated hard. What makes it cost marks is speed and carelessness, not difficulty.

medium90%
easy10%

Difficulty mix across the 124 questions in this skill.

From the bank

Three real linear modeling / word problems questions

Each one explains the credited answer and why every other option fails.

Algebra · medium

Printshop bright meter routing setup card offers a monthly plan for science lab rubrics from the later group that costs $30 plus $0.12 per ticket. A pay-as-you-go plan costs $0.30 per ticket and has no monthly fee. For approximately how many tickets will the two plans cost the same?

  1. A187
  2. B147
  3. C100
  4. D167correct
Why D is correct — and why the others are not

Set the costs equal: 30 + 0.12u = 0.30u. Then 30 = 0.18u, so u is approximately 167. The calculation or reading check points back to Linear modeling / word problems. A final check is identifying the constant term before interpreting the model.

A. This value results from dividing the fixed fee by the higher rate instead of by the difference between the rates

B. This value results from dividing the fixed fee by the higher rate instead of by the difference between the rates

C. This value results from dividing the fixed fee by the higher rate instead of by the difference between the rates

Algebra · easy

Festival evening ladder shelving estimate offers a monthly plan for vaccine clinic signs from the first set examined that costs $18 plus $0.12 per entry. A pay-as-you-go plan costs $0.30 per entry and has no monthly fee. For approximately how many entrys will the two plans cost the same?

  1. A120
  2. B80
  3. C60
  4. D100correct
Why D is correct — and why the others are not

Set the costs equal: 18 + 0.12u = 0.30u. Then 18 = 0.18u, so u is approximately 100. The calculation or reading check points back to Linear modeling / word problems. A final check is matching the result to the correct coordinate or parameter.

A. This value results from dividing the fixed fee by the higher rate instead of by the difference between the rates

B. This value results from dividing the fixed fee by the higher rate instead of by the difference between the rates

C. This value results from dividing the fixed fee by the higher rate instead of by the difference between the rates

Algebra · medium

A coordinator comparing costs for bike-share docks from the newer records finds that one option costs $36 before adding $0.18 per minute; another option costs only $0.40 per minute. What number of minutes makes the costs approximately equal?

  1. A184
  2. B164correct
  3. C144
  4. D90
Why B is correct — and why the others are not

Set the costs equal: 36 + 0.18u = 0.40u. Then 36 = 0.22u, so u is approximately 164. This matches the evidence or condition involving Linear modeling / word problems. A final check is comparing the computed value with the setup's units.

A. This value results from dividing the fixed fee by the higher rate instead of by the difference between the rates

C. This value results from dividing the fixed fee by the higher rate instead of by the difference between the rates

D. This value results from dividing the fixed fee by the higher rate instead of by the difference between the rates

124 questions on this skill, free to start.

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FAQ

Linear Modeling / Word Problems questions

How do I turn a word problem into an equation?

Find the one-off amount (the constant) and the per-unit amount (the coefficient), then name the variable in the units the question uses.

What trips people up?

Dividing by the wrong rate, or attaching the fixed fee to the variable instead of leaving it constant.
Last reviewed 2026-08-28. Format and scoring facts sourced to College Board. Question counts describe the PrepScore bank, not the exam.
Same domain
Systems of Linear Equations135 questionsLinear Equations in One Variable128 questionsLinear Equations in Two Variables127 questionsLinear Functions90 questions

Practise linear modeling / word problems until the trap stops working.

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