Writing a two-variable equation from context. Game on.

Writing a two-variable equation from context is a grade 9 math skill aligned to Common Core standard HSA.CED.A.2: create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. Below are 8 practice questions with answers and step-by-step explanations, drawn from the 10 writing a two-variable equation from context problems our math games drill.

CCSS HSA.CED.A.210 questions in the bank
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Warm-upeasy

A moving crew packs small boxes that weigh 1212 pounds each and large boxes that weigh 3535 pounds each. The crew packs xx small boxes and yy large boxes with a combined weight of 470470 pounds. Which equation represents this situation?

The small boxes weigh 12x12x pounds in all and the large boxes weigh 35y35y pounds in all. The combined weight is 470470 pounds, so 12x+35y=47012x + 35y = 470.

Mid-gameeasy

A community garden has plots for tomato plants that each use 4.54.5 square meters and plots for herb plants that each use 1.51.5 square meters. The garden uses a total of 3636 square meters for xx tomato plots and yy herb plots. Which equation represents this situation?

The tomato plots use 4.5x4.5x square meters and the herb plots use 1.5y1.5y square meters. The total area used is 3636 square meters, so 4.5x+1.5y=364.5x + 1.5y = 36.

Mid-gameeasy

A school fundraiser sells adult tickets for $18\text{\char36}18 each and child tickets for $7\text{\char36}7 each. The school sells xx adult tickets and yy child tickets for a total of $516\text{\char36}516. Which equation represents this situation?

Adult tickets contribute 18x18x dollars and child tickets contribute 7y7y dollars. The total amount collected is 516516 dollars, so 18x+7y=51618x + 7y = 516.

Mid-gameeasy

A cafeteria fills small drink jugs that hold 2.52.5 gallons each and large drink jugs that hold 55 gallons each. The cafeteria fills xx small jugs and yy large jugs with a total of 47.547.5 gallons. Which equation represents this situation?

The small jugs hold 2.5x2.5x gallons in all and the large jugs hold 5y5y gallons in all. The total volume is 47.547.5 gallons, so 2.5x+5y=47.52.5x + 5y = 47.5.

Mid-gameeasy

At a craft fair, making a pair of earrings takes 1212 minutes and making a bracelet takes 2020 minutes. A vendor spends a total of 280280 minutes making xx pairs of earrings and yy bracelets. Which equation represents this situation?

Making xx pairs of earrings takes 12x12x minutes and making yy bracelets takes 20y20y minutes. The total time is 280280 minutes, so 12x+20y=28012x + 20y = 280.

Mid-gameeasy

A theater sells adult tickets for $32\text{\char36}32 each and student tickets for $15\text{\char36}15 each. The theater sells xx adult tickets and yy student tickets for a total of $2,840\text{\char36}2{,}840. Which equation represents this situation?

Adult tickets contribute 32x32x dollars and student tickets contribute 15y15y dollars. The total ticket sales are 2,8402{,}840 dollars, so 32x+15y=2,84032x + 15y = 2{,}840.

Mid-gamemedium

A factory builds two kinds of parts. Part A takes 0.750.75 hours to assemble and part B takes 1.251.25 hours to assemble. Workers spend a total of 17.517.5 hours assembling xx of part A and yy of part B. Which equation represents this situation?

Assembling xx of part A takes 0.75x0.75x hours and assembling yy of part B takes 1.25y1.25y hours. The total assembly time is 17.517.5 hours, so 0.75x+1.25y=17.50.75x + 1.25y = 17.5.

Buzzer beatermedium

A landscaper plants shrubs that each take 1.81.8 hours to install and trees that each take 3.23.2 hours to install. The landscaper spends a total of 22.422.4 hours installing xx shrubs and yy trees. Which equation represents this situation?

Installing xx shrubs takes 1.8x1.8x hours and installing yy trees takes 3.2y3.2y hours. The total installation time is 22.422.4 hours, so 1.8x+3.2y=22.41.8x + 3.2y = 22.4.

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