Question

A local charity held a crafts fair selling donated, handmade items. Total proceeds from the were $1,380. A total of 72 items were sold, some at $15 each and the rest at $25 each. Let x be the number of $15 items and y the number of $25 items. How many items sold $25?

Answer 1

We are given that X+Y=72 and $15X+$25Y=$1380.
Solve for one variable by expressing it in terms of the other. Let's solve for Y (yes we could solve for X but it's arbitrary).
Use first equation, x+y=72. Therefore x=72-y. Let's plug (72-y) into second equation everywhere x appears.
15(72-y) + 25y = 1380. Now solve for y:
1080-15y+25y=1380. 10y=300. y=30. If x+y=72, then x=72-30 or x=42.
Let's check it. X+y=72. 42+30=72. Right answer!

Answer 2

Answer: 30

This is the CORRECT answer!

Explanation:

System: x + y =72 and 15x + 25y =1,380

Solve the first equation for x:

x + y= 72

x = 72 - y

Substitute 72 - y for x in the second equation:

15(72 - y ) + 25y = 1,380

1,080 - 15y + 25y = 1,380

1,080 + 10y = 1,380

10y = 300

y = 30

So 30 items were sold at $25.