The cost of 8 muffins and 2 quarts of milk is $18. The cost of 3 muffins and 1 quart of mil is $7.50. How much does 1 muffin and 1 quart of milk cost?

Answer 1

First set up each part of the word problem as an equation.

8m + 2q = 18

3m + 1q = 7.5

Since you cannot solve an equation with two variables (letters), you need to use one of the equations to get rid of a variable. Let's change the second one to figure out what "q" is.

3m + q = 7.5

Subtract 3m from both sides: q = -3m + 7.5

Now you can plug in = -3m + 7.5 to the first equation instead of q.

8m + 2q = 18: 8m + 2(-3m + 7.5) = 18

Distribute the 2: 8m + -6m + 15 = 18

Combine like terms: 2m + 15 = 18

Subtract 15 from both sides: 2m = 3

Divide both sides by 2: m = 1.5

Therefore, Muffins cost $1.50 each.

Now, plug in 1.5 for m in one of the equations: 3m + q = 7.5

3(1.5) + q = 7.5

4.5 + q = 7.5

Subtract 4.5 from both sides: q = 2

Milk costs $2 per quart.