How to solve the systems of 3 equations

Question

Sally is going to buy a total of 11 new items at Target. She is going to buy jeans, dresses, and

shoes. She is going to spend exactly $460 and has discovered that jeans are $25, dresses are $50,

and shoes are $40. She is also going to buy twice as many shoes as jeans. Find out how many

jeans, how many shoes, and how many dresses she will buy?

Answer 1

Let j be the number of jeans, d be the number of dresses and s be the number of pairs of shoes.

Assuming the problem meant pairs of shoes.

There are 3 unknowns so we need 3 equations.

j + d + s = 11

25j +50d + 40s = 460

s = 2j

Using substitution

j + d + (2j) = 3j + d = 11 --> d = 11-3j

25j + 50(11-3j) + 40(2j) = 25j +550-150j+80j = 460

-45j = -90

j = 2

s = 2j = 4

d = 11-6 = 5