Question

Rhonda took $20 with her to spend on popcorn and candy for herself and her friends at the movie theater.The price for each bag of popcorn was $5. The price of each box of candy was half the price of a bag ofpopcorn.(a) Create an equation and sketch the graph that represents the number of each she can purchase. Useone axis to represent the number of bags of popcorn and the other axis to represent the number ofcandy. Be sure to clearly label the intercepts.(b) In words, explain your graph and what the intercepts mean in context of the situation.

Answer 1

The total of money that Ronda will spend is $20.

We know the popcorn and candy values:

Each bag of popcorn cost $5

The price of each box of candy cost = Half of the popcorn price.

If the popcorn cost $5, the candy box is $5/2 = $2.5.

a.

Set popcorn as the y axis and candy box as the x-axis.

Let's make the equation.

Set y for each popcorn

Set x for each candy box

Then:

5y + 2.5x = 20

To sketch the graph.

Let's find the y-intercept:

To find the y-intercept, set x=0

`5y+2.5(0)=20`
`5y\text{ = 20}`

Solve the equation for y:

Divide both sides by 5

`(5y)/(5)=(20)/(5)`
`y\text{ = 4}`

Now, to find the x-intercept, set y =0

`5(0)+2.5x\text{ = 20}`
`2.5x=20`

Divide both sides by 2.5:

`(2.5x)/(2.5)=(20)/(2.5)`
`x=8`

Therefore, the graph would be like this:

b.

The graph represents the popcorn and candy box that Rhonda can buy, e.g.

If she buys 4 candy boxes, she will afford to buy 2 popcorns.

The y-intercept represents the total of popcorn bags that Rhonda can buy with $20, so she could buy 4 popcorns boy nono of candy boxes.

The x-intercept represents the total of candy boxes that Rhonca can boy with $20. Then. Rhonda could buy 8 candy boxes but none of the popcorn bags.

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