How much of each ingredient did you buy?

Question

the meat cost $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 potatoe. 

Answer 1

Let x = the no. of potatoes bought, then 2x = the no. of carrots bought. Now, let y = the amount of meat purchased. We can form a system of equations as such:

 

x + 2x + y = 13.5 (the total amount of food purchased)

6y + 3x + 2x = 48.5 (the total cost of the food)

 

3x + y = 13.5

5x + 6y = 48.5    when we combine like terms

 

Let's multiply the top equation by 6 and subtract the two equations:

 

18x + 6y = 81

-(5x + 6y = 48.5)

 

13x = 32.5

x = 2.5

 

That means 2.5 lb of potatoes were bought, 2 * 2.5 = 5 lb of carrots were bought, and we now need to determine how much meat was purchased. Let's plug x = 2.5 into the equation 3x + y = 13.5

 

3(2.5) + y = 13.5

7.5 + y = 13.5

y = 6

 

Hence, 6 lb of meat was bought.