Question

Cody and Katie bought reusable bags for a fundraiser. Cody bought 4

small bags and 2 large bags and spent
$52. Katie bought 1 large bag and 3
small bags and spent $32. How much
was each bag?

Answer 1

The cost of a small bag is approximately $6.67 and the cost of a large bag is approximately $8.44.

Step-by-step explanation:

Let's assign variables to represent the cost of a small bag and a large bag.

Let's say the cost of a small bag is x and the cost of a large bag is y.

According to the given information, we can set up two equations:

Cody bought 4 small bags and 2 large bags for a total cost of $52:

4x + 2y = 52

Katie bought 1 large bag and 3 small bags for a total cost of $32:

x + 3y = 32

To solve these equations, we can use the substitution or elimination method. Let's solve it using the elimination method:

1. Multiply the first equation by 3 and the second equation by 4 to make the coefficients of y the same:
2. 12x + 6y = 156
3. 4x + 12y = 128
4. Subtract the second equation from the first to eliminate y:
5. 12x + 6y - (4x + 12y) = 156 - 128
6. 8x - 6y = 28
7. Combine like terms:
8. 8x - 6y = 28
9. Add this equation to the second equation (x + 3y = 32) to solve for x:
10. 8x - 6y + (x + 3y) = 28 + 32
11. 9x = 60
12. Divide both sides by 9 to find the value of x:
13. x = 6.67
14. Substitute the value of x into x + 3y = 32 to solve for y:
15. 6.67 + 3y = 32
16. 3y = 25.33
17. y = 8.44

Therefore, the cost of a small bag is approximately $6.67 and the cost of a large bag is approximately $8.44.