SAT Math Word Problem: Mulch and Soil
This is the complete problem, not a summary. You will see the original equation, full wording, every answer choice, the keyed answer, and the exact algebra that gets you there.
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Question banks: October 2026 Math question bank
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The given equation represents the volume of mulch x, in cubic feet, and the volume of soil y, in cubic feet, in a mixture of mulch and soil that weighs 290 pounds. If the volume of soil in the mixture is 2 cubic feet, what is the volume of mulch in the mixture, in cubic feet?
Correct answer: A) 4 cubic feet. TTA choice record 131517 is marked correct.
Step-by-step solution
The problem tells you that the soil volume is 2 cubic feet. Because y represents soil, set y equal to 2.
y = 2Do not replace x. The question asks for mulch, and the equation defines mulch as x.
Since 81 × 2 = 162, the soil contributes 162 pounds to the total represented by the equation.
The variable x represents cubic feet of mulch, so the final answer is 4 cubic feet.
Check the answer in the original equation
Substitute both known values:
32(4) + 81(2) = 128 + 162 = 290
The left side equals the stated total of 290, so the answer checks.
Why students miss this question
Mixing up the variables
The sentence defines mulch as x and soil as y. Writing “soil = 2” without connecting it to y can lead you to substitute into the wrong place.
Dividing too early
You cannot divide 290 by 32 immediately because the soil term, 81y, is also part of the total. Substitute and subtract that contribution first.
Ignoring units
The equation uses pounds for total weight, but the requested value is a volume. The answer is not “4 pounds.” It is 4 cubic feet of mulch.
Calculator check
In Desmos or a calculator, enter (290 − 81(2)) / 32. The result is 4. Use this as a check, not as a substitute for identifying what x and y mean.
Practice the exact skill next
Work on interpreting linear models while this method is fresh. Predict what each variable means before touching the calculator.
Practice linear-equation word problems Review another worked SAT Math problem Create a free accountFrequently asked questions
What test and question is this mulch-and-soil problem from?
In the TTA database, it is DSAT Math September 2025 US Version C, Module 2, Question 3. The canonical TTA source question is 131516.
What is the correct answer?
The correct answer is 4 cubic feet. Substitute y = 2, simplify to 32x + 162 = 290, subtract 162, and divide 128 by 32.
Can I solve this SAT word problem with Desmos?
Yes. Enter (290 − 81(2)) / 32 to calculate x. You still need to read the prompt carefully enough to know that y is the soil volume and equals 2.
Frequently Asked Questions
What test and question is this mulch-and-soil problem from?
In the TTA database, it is DSAT Math September 2025 US Version C, Module 2, Question 3. The canonical TTA source question is 131516.
What is the correct answer?
The correct answer is 4 cubic feet. Substitute y = 2, simplify to 32x + 162 = 290, subtract 162, and divide 128 by 32.
Can I solve this SAT word problem with Desmos?
Yes. Enter (290 - 81(2)) / 32 to calculate x. You still need to identify y as the soil volume.