Question

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.

Explanation:

Step1: Define variables

Let $x$ = price of 1 flashlight, $y$ = price of 1 sleeping bag.

Step2: Set up equations

First group: $7x + 11y = 299$
Second group: $8x + 11y = 304$

Step3: Eliminate $y$ via subtraction

Subtract first equation from second:
$$(8x + 11y) - (7x + 11y) = 304 - 299$$
$$x = 5$$

Step4: Solve for $y$

Substitute $x=5$ into first equation:
$$7(5) + 11y = 299$$
$$35 + 11y = 299$$
$$11y = 299 - 35$$
$$11y = 264$$
$$y = \frac{264}{11} = 24$$

Answer:

The price of one flashlight is $\$5$, and the price of one sleeping bag is $\$24$.