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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1
Warm-upeasy
A moving crew packs small boxes that weigh 12 pounds each and large boxes that weigh 35 pounds each. The crew packs x small boxes and y large boxes with a combined weight of 470 pounds. Which equation represents this situation?
The small boxes weigh 12x pounds in all and the large boxes weigh 35y pounds in all. The combined weight is 470 pounds, so 12x+35y=470.
2
Mid-gameeasy
A community garden has plots for tomato plants that each use 4.5 square meters and plots for herb plants that each use 1.5 square meters. The garden uses a total of 36 square meters for x tomato plots and y herb plots. Which equation represents this situation?
The tomato plots use 4.5x square meters and the herb plots use 1.5y square meters. The total area used is 36 square meters, so 4.5x+1.5y=36.
3
Mid-gameeasy
A school fundraiser sells adult tickets for $18 each and child tickets for $7 each. The school sells x adult tickets and y child tickets for a total of $516. Which equation represents this situation?
Adult tickets contribute 18x dollars and child tickets contribute 7y dollars. The total amount collected is 516 dollars, so 18x+7y=516.
4
Mid-gameeasy
A cafeteria fills small drink jugs that hold 2.5 gallons each and large drink jugs that hold 5 gallons each. The cafeteria fills x small jugs and y large jugs with a total of 47.5 gallons. Which equation represents this situation?
The small jugs hold 2.5x gallons in all and the large jugs hold 5y gallons in all. The total volume is 47.5 gallons, so 2.5x+5y=47.5.
5
Mid-gameeasy
At a craft fair, making a pair of earrings takes 12 minutes and making a bracelet takes 20 minutes. A vendor spends a total of 280 minutes making x pairs of earrings and y bracelets. Which equation represents this situation?
Making x pairs of earrings takes 12x minutes and making y bracelets takes 20y minutes. The total time is 280 minutes, so 12x+20y=280.
6
Mid-gameeasy
A theater sells adult tickets for $32 each and student tickets for $15 each. The theater sells x adult tickets and y student tickets for a total of $2,840. Which equation represents this situation?
Adult tickets contribute 32x dollars and student tickets contribute 15y dollars. The total ticket sales are 2,840 dollars, so 32x+15y=2,840.
7
Mid-gamemedium
A factory builds two kinds of parts. Part A takes 0.75 hours to assemble and part B takes 1.25 hours to assemble. Workers spend a total of 17.5 hours assembling x of part A and y of part B. Which equation represents this situation?
Assembling x of part A takes 0.75x hours and assembling y of part B takes 1.25y hours. The total assembly time is 17.5 hours, so 0.75x+1.25y=17.5.
8
Buzzer beatermedium
A landscaper plants shrubs that each take 1.8 hours to install and trees that each take 3.2 hours to install. The landscaper spends a total of 22.4 hours installing x shrubs and y trees. Which equation represents this situation?
Installing x shrubs takes 1.8x hours and installing y trees takes 3.2y hours. The total installation time is 22.4 hours, so 1.8x+3.2y=22.4.
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