Question

A local restaurant owner can purchase tea for $16 per pound and coffee for $8 per pound. His budget does not allow him to spend more than $280 on coffee and tea. Which graph shows the possible combinations of pounds of tea, x, and pounds of coffee, y, that the restaurant owner can purchase? 6)

Answer 1

In order to determine which is the graph, write the given situation as a inequality. If x is the number of pound of tea and y the number of pounds of coffe, for x pounds of tea and y pounds of coffe, the cost is 16x + 8y.

Moreover, The restaurant owner can not spend more than $280. Then, the number of x pounds of tea and y pounds of coffe are given by the following inequality:

16x + 8y ≤ 280

solve the previous inequality for y, as follow:

16x + 8y ≤ 280 subtract 16x both sides

8y ≤ -16x + 280 divide by 8 both sides

y ≤ -2x + 35

The previous result means that the number of pounds of coffe must belower or equal than -2x + 35. The limit for the values of y is given by the following equation of the line:

y = -2x + 35

the y and x intercepts of the line are:

y-intercept:

y = -2(0) + 35 = 35

y = 35

x-intercept:

0 = -2x + 35

2x = 35

x = 35/2

x = 17.5

Form the given answer choices, you can notice that option B because this graph has the same x and y intercepts we have found.