A meat distributor paid $2.75 per pound for hamburger and $4.50 per pound for ground sirloin. How many pounds of each did he use to make 75 pounds of meat mixture that will cost $3.24 per pound?

The number of pounds of hamburger meat = x = 54 pounds.

The number of pounds of ground sirloin = y = 21 pounds

Step-by-step explanation:

Let the number of pounds of hamburger meat = x

the number of pounds of ground sirloin = y

How many pounds of each did he use to make 75 pounds of meat mixture that will cost $3.24 per pound?

x + y = 75 Equation 1

x = 75 - y

A meat distributor paid $2.75 per pound for hamburger and $4.50 per pound for ground sirloin.

$2.75 × x + $4.50 × y = 75 × $3.24

2.75x + 4.50y = 243

We substitute 75 - y for x

Hence,

2.75(75 - y) + 4.5y = 243

206.25 - 2.75y + 4.5 y = 243

Collect like terms

- 2.75y + 4.5 y = 243 - 206.25

1.75y = 36.75

y = 36.75/1.75

y = 21 pounds

Note

x = 75 - y

x = 75 - 21

x = 54 pounds

Therefore:

The number of pounds of hamburger meat = x = 54 pounds.

The number of pounds of ground sirloin = y = 21 pounds

the value of x is 10