Question

Amy has $30 to spend on snacks and beverages for herself and her friends at the movie theater. The cost for nachos was $5. The cost for each beverage was half the cost of the nachos.

(a) Sketch a graph that represents this situation and label the intercepts. Use one axis to represent the number nachos and the other axis to represent the number of beverages.
(b)Explain your graph.

Answer 1

Amy has $30 to spend on snacks and beverages for herself and her friends at the movie theater. The cost for nachos was $5. The cost for each beverage was half the cost of the nachos

Let x be the number of nachos and y be the number of beverages

The cost for nachos was $5. So the cost of 'x' nachos = 5x

The cost for each beverage was half the cost of the nachos.

The cost of each beverage =
`(5)/(2)= 2.5`

so the cost of y beverage = 2.5 y

Cost of x nachos + cost of y beverage = total amount spend

5x + 2.5y = 30

Now we find x and y intercept

When Amy does not buy any beverages we put y=0

5x + 2.5(0) = 30

5x = 30

x= 6. The x intercept is (6,0)

When Amy does not buy any nachos we put x=0

5(0) + 2.5y = 30

2.5y = 30

y=12. The y intercept is (0,12)

The graph is attached below

(b) The graph is a straight line. From the graph we can see that when Amy does not buy any nachos then she can spend #30 to buy 12 beverages .

when Amy does not buy any beverages then she can spend #30 to buy 6 nachos.