Question

You are ordering shirts for the math club at your school. Short-sleeved shirts cost $10 each. Long-sleeved shirts cost $14 each. You have a budget of $350 for the shirts. The equation $10x+14y=350$ models the total cost, where $x$ is the number of short-sleeved shirts and $y$ is the number of long-sleeved shirts. Graph the equation. Interpret the intercepts

Answer 1

Plot the x-intercepts at (35, 0) and the y-intercepts at (0, 25)) on a graph and draw a line through them.

The cost of short-sleeved shirts per unit = $10

The cost of long-sleeved shirts per unit = $14

The total budget for the shirts = $350

Let the number of short-sleeved shirts = x

Let the number of long-sleeved shirts = y

The total cost equation:

10x + 14y = 350

To graph the equation 10x + 14y = 350, we can first find the intercepts.

To find the x-intercept, we set y = 0 and solve for x: 10x + 14(0) = 350

10x = 350

x = 35

Thus, the x-intercept is at (35, 0).

To find the y-intercept, set x = 0 and solve for y: 10(0) + 14y = 350

14y = 350

y = 25

Thus, the y-intercept is at (0, 25).

The line of the graph represents all combinations of short-sleeved and long-sleeved shirts that be purchased per the of $350.

Thus, the x-intercept is where the number of short-sleeved shirts is maximized given the budget, and the y-intercept is where the number of long-sleeved shirts is maximized given the budget.