Question

Brian's Bakery sells loaves of Italian bread for $3.50 and loaves of rye bread for $2.80. Brian's goal is to bring in $420 per day from sales of these two items.

write a linear equation in standard form that describes the problem :
what is the x-intercept :
what is the y-intercept :

Answer 1

The linear equation that represents Brian's sales goal is 3.50x + 2.80y = 420. The x-intercept is (120, 0), meaning 120 loaves of Italian bread need to be sold with no Rye bread being sold. The y-intercept is (0, 150), meaning 150 loaves of Rye bread need to be sold with no Italian bread being sold.

Step-by-step explanation:

Let's consider that x represents the number of loaves of Italian bread sold at $3.50 each, and y represents the number of loaves of Rye bread sold at $2.80 each.

Brian's goal is to make $420 per day. To express this as a linear equation in standard form, we combine the products of the prices and quantities for both types of bread:
3.50x + 2.80y = 420

To find the x-intercept, we set y to 0 and solve for x:
3.50x = 420 → x = 120

The x-intercept is thus the point (120, 0), which means if Brian sells only Italian bread, he can sell 120 loaves.

To find the y-intercept, we set x to 0 and solve for y:
2.80y = 420 → y = 150

The y-intercept is (0, 150), indicating that if only Rye bread is sold, 150 loaves would meet the sales goal.