Question

In a discount clothing store, all sweaters are sold at one fixed price and all shirts are sold at another fixed price. If one sweater and four shirts cost $55, while four sweaters and five shirts costs $110, find the price of one sweater and the price of one shirt.

Answer 1

Price of one shirt: $10

Price of one sweater: $15

Explanation:

The price of one sweater - x

The price of one shirt - y

From what the problem states, we can assume:

x + 4y = 55

4x + 5y = 110

Multiply both sides of x +4y = 55 by four. This results in 4x + 16y = 220. We then subtract 16y on both sides, resulting in 4x = 220 - 16y. We then insert this into the other equation, which, as a reminder, is 4x + 5y = 110. We replace 4x with 220 - 16y, which results in 220 - 16y + 5y = 110. Now, we can solve it.

1. 220 - 16y + 5y = 110
2. 220 - 11y = 110
3. 110 - 11y = 0
4. 110 = 11y
5. y = $10

Now that we have found out the value of y, we can replace all instances of y in the first equation.

1. x + 4y = 55
2. x + 40 = 55
3. x = $15