Question

Suppose you have $30 to spend on a bag is tootsie rolls that are worth $3 and bags of lolli-pops worth $5.If you have to use all of their money , What combinations of candy bags can they buy ? Construct a liner equation and find /explain the y -intercept,x-intercept ,and slope

Answer 1

Part a)
`3x+5y=30`

Part b) see the explanation

Part c) see the explanation

Explanation:

Part a) Construct a liner equation

Let

x ----> the number of bags of tootsie rolls

y ----> the number of bags of lolly-pops

we know that

The number of bags of tootsie rolls bought multiplied by their price ($3) plus the number of bags of lolly-pops bought multiplied by their price ($5) must equal $30

so

The linear equation that represent this problem is

`3x+5y=30`

Part b) Find the intercepts

Find the y-intercept

The y-intercept is the value of y when the value of x s equal to zero

In this context, the y-intercept is the number of bags of lolly-pops that i can buy when the number of bags of tootsie rolls is equal to zero

For x=0

`3(0)+5y=30`

`y=6`

The y-intercept is the point (0,6)

so

I can buy 6 bags of lolly-pops and 0 bags of tootsie rolls

Find the x-intercept

The x-intercept is the value of x when the value of y s equal to zero

In this context, the x-intercept is the number of bags of tootsie rolls that i can buy when the number of bags of lolly-pops is equal to zero

For y=0

`3x+5(0)=30`

`x=10`

The x-intercept is the point (10,0)

so

I can buy 10 bags of tootsie rolls and 0 bags of lolly-pops

Part c) Find the slope

we have

`3x+5y=30`

isolate the variable y

`5y=-3x+30`

`y=-(3)/(5)x+6`

The slope is m=-3/5 ---> is negative because is a decreasing function

That means ---> For every three less lollipops you get, you can have 5 more tootsie rolls