Writing systems from context. Game on.

Writing systems from context is a grade 9 math skill aligned to Common Core standard HSA.CED.A.3: represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context. Below are 8 practice questions with answers and step-by-step explanations, drawn from the 10 writing systems from context problems our math games drill.

CCSS HSA.CED.A.310 questions in the bank
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Warm-upeasy

Lena is ℓ\ell years old and her brother is bb years old. Lena is 22 times as old as her brother, and the sum of their ages is 3636. Which system of equations represents this situation?

Lena is 22 times as old as her brother, so ℓ=2b\ell = 2b. The sum of their ages is 3636, so ℓ+b=36.\ell + b = 36\textsf{.}

Mid-gameeasy

A farm has cc cows and hh horses. There are 44 times as many cows as horses, and there are 6060 animals in total. Which system of equations represents this situation?

There are 44 times as many cows as horses, so c=4hc = 4h. The total number of animals is 6060, so c+h=60.c + h = 60\textsf{.}

Mid-gameeasy

Noah has nn trading cards and Sofia has ss trading cards. Noah has 66 times as many cards as Sofia, and together they have 8484 cards. Which system of equations represents this situation?

Noah has 66 times as many cards as Sofia, so n=6sn = 6s. Together they have 8484 cards, so n+s=84.n + s = 84\textsf{.}

Mid-gameeasy

A recipe uses ff cups of flour and ss cups of sugar. The recipe uses 33 times as much flour as sugar, and the flour and sugar together measure 88 cups. Which system of equations represents this situation?

The recipe uses 33 times as much flour as sugar, so f=3sf = 3s. Together they measure 88 cups, so f+s=8.f + s = 8\textsf{.}

Mid-gameeasy

Kai scored kk points and Riley scored rr points in a game. Kai scored 22 times as many points as Riley, and their combined score was 4545 points. Which system of equations represents this situation?

Kai scored 22 times as many points as Riley, so k=2rk = 2r. Their combined score was 4545, so k+r=45.k + r = 45\textsf{.}

Mid-gameeasy

A parking lot has cc cars and tt trucks. There are 77 times as many cars as trucks, and there are 5656 vehicles in the lot. Which system of equations represents this situation?

There are 77 times as many cars as trucks, so c=7tc = 7t. The total number of vehicles is 5656, so c+t=56.c + t = 56\textsf{.}

Mid-gameeasy

Amira has aa stickers and Ben has bb stickers. Amira has 55 times as many stickers as Ben, and together they have 9090 stickers. Which system of equations represents this situation?

Amira has 55 times as many stickers as Ben, so a=5ba = 5b. Together they have 9090 stickers, so a+b=90.a + b = 90\textsf{.}

Buzzer beatereasy

A store sold dd hardcover books and pp paperback books. It sold 33 times as many paperbacks as hardcovers, and it sold 120120 books in all. Which system of equations represents this situation?

It sold 33 times as many paperbacks as hardcovers, so p=3dp = 3d. The total number of books sold is 120120, so d+p=120.d + p = 120\textsf{.}

Tests that cover writing systems from context:
PSAT 8/9NAEPACTLEAP 2025NC EOG/EOC
More Grade 9 skills
Linear systems by substitution (SAT)Solving two-variable linear equations given one valueLinear system word problemsLiteral equations (SAT)Linear system expressionsLiteral quadratic equations (ACT)Linear rule from a function table (ACT)Monomial expression multiplication (SAT)All Grade 9 practice →

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