Question

at a fair, hamburger sell for $3.00 each and hot dogs sell for $1.50 each. the equation 3x+1.5y=30 describes the number of hamburger and hot dogs a family can buy with $30. a.find the intercepts and graph the function b. what does each intercepts represent?

Answer 1

The intercepts of the equation are (10, 0) and (0, 20). The x-intercept represents the number of hamburgers a family can buy with $30, and the y-intercept represents the number of hot dogs a family can buy with $30.

Step-by-step explanation:

To find the intercepts of the equation 3x+1.5y=30, we need to set one of the variables (x or y) to zero and solve for the other variable.

a) Intercept and Interpretation:

• To find the x-intercept, let y = 0 and solve for x: 3x + 1.5(0) = 30. Simplifying the equation gives us 3x = 30, which leads to x = 10. Therefore, the x-intercept is (10, 0).
• To find the y-intercept, let x = 0 and solve for y: 3(0) + 1.5y = 30. Simplifying the equation gives us 1.5y = 30, which leads to y = 20. Therefore, the y-intercept is (0, 20).

b) Each intercept represents a point on the graph where one variable is zero. The x-intercept represents the number of hamburgers a family can buy with $30 if they only buy hamburgers and no hot dogs. The y-intercept represents the number of hot dogs a family can buy with $30 if they only buy hot dogs and no hamburgers.

Answer 2

The answer is five using two step equations