SAT Math formula sheet · all 24 · Algebra · #4 of 24

Mixture problems on the SAT: How It Is Tested

Systems of two linear equations

Mixture Problem diagram for the SAT: Two cups going into one cup. Every cup gets a percent and an amount, and the equation is (percent)(amount) + (percent)(a
What it is really testingTwo cups going into one cup. Every cup gets a percent and an amount, and the equation is (percent)(amount) + (percent)(amount) = (percent)(amount). If one amount is x, the other one is the total minus x.

The question from the sheet

Hard
SAT Algebraanswer A
A sample of a certain solution has a total mass of 60.0 grams and is 40.0% salt by mass. The sample was created by combining two portions of different solutions. The first portion was 25.0% salt by mass and the second portion was 70.0% salt by mass. What was the mass, in grams, of the second portion?
✓20.020.0
B14.014.0
C40.040.0
D28.028.0

How the diagram applies

  1. Fill the boxes: percent times amount for each portion, equal to percent times the total. Let ss be the second portion, so the first is 60−s60 - s.
  2. 0.25(60−s)+0.70s=0.40(60)0.25(60 - s) + 0.70s = 0.40(60)
  3. 15+0.45s=2415 + 0.45s = 24, so s=20s = 20 grams.

Answer: A

That is 1 of 24.

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Common Questions

It comes up as an SAT systems of two linear equations question. Two cups going into one cup. Every cup gets a percent and an amount, and the equation is (percent)(amount) + (percent)(amount) = (percent)(amount). If one amount is x, the other one is the total minus x.

Fill the boxes: percent times amount for each portion, equal to percent times the total. Let s be the second portion, so the first is 60 - s. 0.25(60 - s) + 0.70s = 0.40(60) 15 + 0.45s = 24, so s = 20 grams.

No. The SAT reference sheet is twelve geometry formulas and three notes, and Mixture Problem is not one of them. It is one of the 24 things the test expects you to know without being given them. See what the reference sheet does cover at /blog/sat-math-reference-sheet.