Question

The school band is selling sweatshirts and baseball caps to raise $9000 to attend a band competition. Sweatshirts cost $25 each and baseball caps cost $10 each. The equation 25x + 10y = 9000 models this situation, where x is the number of sweatshirts sold and y is the number of baseball caps. A. Find and interpret the intercepts. B. If 258 sweatshirts are sold, how many baseball caps are sold?

A. Sweatshirt Intercept: 360, Cap Intercept: 900
B. Sweatshirt Intercept: 0, Cap Intercept: 900
C. Sweatshirt Intercept: 0, Cap Intercept: 360
D. Sweatshirt Intercept: 900, Cap Intercept: 0

Answer 1

The sweatshirt intercept is 360, meaning 360 sweatshirts need to be sold without baseball caps to raise $9000. The cap intercept is 900, meaning 900 baseball caps need to be sold without sweatshirts. If 258 sweatshirts are sold, the number of baseball caps needed is 255.

Step-by-step explanation:

The equation given is 25x + 10y = 9000, which models the sale of sweatshirts and baseball caps. To find the intercepts, we set one variable to zero and solve for the other.

To find the sweatshirt intercept, set y to 0: 25x = 9000. Solving for x gives x = 9000 / 25, which simplifies to x = 360. This means if the school band sells only sweatshirts with no baseball caps, they would need to sell 360 sweatshirts to raise $9000.

Similarly, to find the cap intercept, set x to 0: 10y = 9000. Solving for y gives y = 9000 / 10, which simplifies to y = 900. This means if they only sell baseball caps, they need to sell 900 caps to reach their goal.

Now for part B, if 258 sweatshirts are sold, substitute x = 258 into the equation to find y: 25(258) + 10y = 9000, which gives 6450 + 10y = 9000. Subtracting 6450 from both sides gives us 10y = 2550, so y = 255. This means they would need to sell 255 baseball caps in addition to the 258 sweatshirts to meet their goal.