Question

Jack bought x picks costing $30 each and y shovels costing $40 each.In all he spent

$240.
a. Write a function to represent this situation.
b. What are the x- and y-intercepts of the function?
c. What do the intercepts represent?

Answer 1

The function representing the situation is 30x + 40y = 240. The x-intercept is (8, 0) and the y-intercept is (0, 6). The intercepts represent the number of picks and shovels, respectively, that Jack would need to buy if he didn't buy any of the other item.

Step-by-step explanation:

In this situation, the function can be represented as 30x + 40y = 240. Here, x represents the number of picks bought by Jack, and y represents the number of shovels bought. The intercepts of the function can be found by setting x or y equal to 0 and solving for the other variable.

1. x-intercept: When y = 0, we have 30x = 240, which simplifies to x = 8. So, the x-intercept is (8, 0).
2. y-intercept: When x = 0, we have 40y = 240, which simplifies to y = 6. So, the y-intercept is (0, 6).

The x-intercept represents the number of picks Jack would need to buy if he didn't buy any shovels, and the y-intercept represents the number of shovels Jack would need to buy if he didn't buy any picks.