For a party, you are cooking a large amount of stew that has meat, potatoes, and carrots. The meat costs $6 per pound, the potatoes cost $3 per pound, and the carrots cost $1 per pound. You spend $48.50 on 13.5 pounds of food. You buy twice as many carrots as potatoes.
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I need 3 equations that represent how much food I bought (in a triple variable systematic way)

Question

For a party, you are cooking a large amount of stew that has meat, potatoes, and carrots. The meat costs $6 per pound, the potatoes cost $3 per pound, and the carrots cost $1 per pound. You spend $48.50 on 13.5 pounds of food. You buy twice as many carrots as potatoes.
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I need 3 equations that represent how much food I bought (in a triple variable systematic way)

anonymous · Answer

Let x be number of pounds of meat

anonymous · Answer

let 
x = lb of meat
y = lb of potatoes
z = lb of carrots

x + y + z = 13.5
6x + 3y + z = 48.5

z = 2y

x + y + 2y = 13.5
x + 3y = 13.5

x = 13.5-3y

6(13.5-3y) + 3y + 2y = 48.5
81 - 18y + 5y = 48.5
81 - 48.5 = 13y
32.5 = 13y
2.5 = y

x = 13.5 - 3y
x = 13.5 -3*2.5
x = 13.5 - 7.5
x = 6

z = 2y
z = 2*2.5
z = 5