Question

You and a friend are selling t-shirts and socks to raise money for a school trip for Springfield Elementary. You sold 20 t-shirts and 11 pairs of socks and made $295. Your friend sold 10 t-shirts and 15 pairs of socks and made $195. Write a system of equations that could be used to solve for the price of one t-shirt and one pair of socks.

Answer 1

To find the price of one t-shirt and one pair of socks, we can set up a system of equations using the given information. The price of one t-shirt is $12 and the price of one pair of socks is $5.

Step-by-step explanation:

To find the price of one t-shirt and one pair of socks, we can set up a system of equations using the given information. Let x be the price of one t-shirt and y be the price of one pair of socks.

From the information given:

20x + 11y = 295 (Equation 1)

10x + 15y = 195 (Equation 2)

We can use these two equations to solve for x and y.

1. First, we can multiply Equation 1 by 10 and Equation 2 by 20 to eliminate the x variable.
2. Multiply Equation 1 by 10: 200x + 110y = 2950
3. Multiply Equation 2 by 20: 200x + 300y = 3900
4. Subtract Equation 2 from Equation 1 to eliminate the x variable:

200x + 110y - (200x + 300y) = 2950 - 3900

-190y = -950

Divide both sides of the equation by -190:

y = 5

Now, substitute the value of y into either of the original equations to solve for x. Let's use Equation 1:

20x + 11(5) = 295

20x + 55 = 295

Subtract 55 from both sides:

20x = 240

Divide both sides by 20:

x = 12

Therefore, the price of one t-shirt is $12 and the price of one pair of socks is $5.