Systems of Equations Three Variables Word Problems

Three friends are making homecoming mums before the big game. When all three friends are working, they produce 6 mums per hour. When only Friend B and Friend C are working, they make 5 mums per hour. When only Friend A and Friend B are working, they make 4 mums per hour.

What system of equations represents the scenario above?

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CCSS.HSA.CED.A.3

Maya bought a dozen specialty donuts at the bakery for $18. She purchased a mixture of frosted donuts for $2 each, glazed donuts for $1 each, and custard filled donuts for $5 each. If Maya purchased twice as many frosted donuts as custard filled donuts, how many of each type of donut did she buy?

• 3 frosted, 8 glazed, and 1 custard

• 4 frosted, 7 glazed, and 1 custard

• 2 frosted, 9 glazed, and 1 custard

• 1 frosted, 7 glazed, 4 custard

The combined age of three sisters is 74. The eldest sister’s age is twelve less than the sum of her sisters’ ages. The middle sister is five years older than the youngest. What system of equations represents this scenario?

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CCSS.HSA.CED.A.3

Three brothers are taking down a wooden fence, including removing the nails from the boards. When all three brothers are working, they break down 16 feet of fencing per hour. When only the eldest and youngest brothers are working, they take down 10 feet per hour. The middle and youngest brothers manage to take down 8 feet per hour when working together. Which system of equations represents this scenario?

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CCSS.HSA.CED.A.3

Natalie purchased 6 spiral notebooks at the beginning of the school year for $16. She bought a combination of super-value 1-subject spirals, traditional 3-subject spirals, and dura-tough 5-subject spirals for one dollar, three dollars, and seven dollars each, respectively. If she

purchased three times as many super-value spirals as dura-tough spirals, how many of each type of spiral notebook did Natalie purchase?

• 1 super-value, 2 traditional, and 3 dura-tough spirals

• 2 super-value, 2 traditional, and 2 dura-tough spirals

• 4 super-value, 1 traditional, and 1 dura-tough spirals

• 3 super-value, 2 traditional, and 1 dura tough spirals

Horatio has 57 coins consisting of nickels, dimes, and quarters. He has twice as many dimes as nickels. If the coins are worth a total of $7.25, which system of equations is used to determine how many of each coin Horatio has?

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CCSS.HSA.CED.A.3

Aaron has 45 coins consisting of nickels, dimes, and quarters. He has three times as many dimes as quarters. If the coins are worth a total of $5.75, which system of equations is used to determine how many of each coin Aaron has?

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Nelly has 31 coins consisting of nickels, dimes, and quarters. She has twice as many nickels as quarters. If the coins are worth a total of $3.45, which system of equations is used to determine how many of each coin Nelly has?

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