Question

10. Two school groups went shopping for

camping supplies at the same store. The
first group spent $299 on 7 flashlights and
11 sleeping bags. The second group spent
$304 on 8 flashlights and 11 sleeping bags.
Write and solve a system of equations
using elimination to find the price of each
flashlight and each sleeping bag.

Answer 1

The price of each flashlight is 5 and the price of each sleeping bag is 24.

Step-by-step explanation:

To find the price of each flashlight and each sleeping bag, we can create a system of equations using the information given:

Let x be the price of each flashlight and y be the price of each sleeping bag.

We can set up two equations:

From the first group: 7x + 11y = 299

From the second group: 8x + 11y = 304

To solve this system of equations using elimination, we can multiply the first equation by 8 and the second equation by 7, then subtract the two equations:

56x + 88y = 2392

56x + 77y = 2128

Subtracting the two equations gives: 11y = 264

Therefore, the price of each sleeping bag is 24.

Substituting the value of y into one of the original equations, we can solve for the price of each flashlight:

7x + 11(24) = 299

7x + 264 = 299

7x = 35

x = 5

The price of each flashlight is 5.