Question

I am shopping for stocking stuffers. I have $45 to spend and can buy bags of candy for $2.50 each and fuzzy socks for $7.50. 1. Write an equation to represent the situation.2. Find the x and y intercepts and explain what they represent.

Answer 1

Assuming that all $45 will be spent, no more no less, is will be equal to the sum of what is spent on candy and socks.

Ley x represent the number of bag of candy bought and let y be the number of fuzzy socks bought.

Since each bag of candy costs $2.50, the total spent on candy is:

`2.5x`

Since each fuzze sock costs $7.50, the total spent on socks is:

`7.5y`

Adding them, we have to get a value equal to the total spent, $45, so this is the equation that represents the situation:

`2.5x+7.5x=45`

The x intercept is the x value when y = 0:

`\begin{gathered} 2.5x+7.5\cdot0=45 \\ 2.5x=45 \\ x=(45)/(2.5) \\ x=18 \end{gathered}`

The y intercept is the y value when x = 0:

`\begin{gathered} 2.5\cdot0+7.5y=45 \\ 7.5y=45 \\ y=(45)/(7.5) \\ y=6 \end{gathered}`

Since x is the number of bag of candy bought and y is the number of fuzzy socks bought:

- the x-intercept represents the situation where all the money was spent on bag of candy and no fuzzy sock was bought.

- the y-intercept represents the situation where all the money was spent on fuzzy socks and no bag of candy was bought.