system of equations

Question

On a recent trip to the convenience​ store, you picked up 2 gallons of​ milk, 6 bottles of​ water, and 6 snack-size bags of chips. Your total bill​ (before tax) was $25.60. If a bottle of water costs twice as much as a bag of​ chips, and a gallon of milk costs ​$1.80 more than a bottle of​ water, how much does each item​ cost?

Answer 1

Define your variables:

m = milk

w = water

c = chips

The total cost for 2 milks, 6 waters, and 6 chips was 25.60, so the equation would be

2m + 6w + 6c = 25.60

If a bottle of water is twice as much as a bag of chips, translate that into the equation w = 2c.

Solve this equation for c:

c = .5w

If a gallon of milk costs 1.80 more than a bottle of water, translate that into m = w + 1.80.

Substitute .5w in for c and w + 1.80 in for m in the first equation:

2(w+1.80) + 6w + 6(.5w) = 25.60

Distribute and simplify:

2w + 3.60 + 6w + 3w = 25.60;     11w + 3.60 = 25.60

Solve for w:

w = 2

Substitute w = 2 into the original equations:

c = .5(2) = 1.00

m = 2 + 1.80 = 3.80.

Milk was $3.80, water was $2.00, and chips were $1.00.