Jack is going to make rainbow sherbet punch by mixing ginger ale and cranberry j

Question

Jack is going to make rainbow sherbet punch by mixing ginger ale and cranberry juice. Regina will then float a quart of rainbow sherbet on top. Ginger ale costs $2 per gallon, and cranberry juice costs $5 per gallon. The Honors Society has budgeted $120 for the ginger ale and juice. What are the different amounts of ginger ale and juice that Jack and Regina can buy with $120 and have no money left over

Define the variables.

Create an equation to model the situation

What is the x, y-intercept and what do they mean

Explanation / Answer

Let number of gallons of gingre ale= x

Let number of gallons of cranberry juice = y

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then cost equation will be 2x+5y=120

or 5y=-2x+120

or y=-(2/5)x+24

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"no money left over" means any solution to above equation will be answer.

for example take x=5 we get:

y=-(2/5)*5+24=-2+24=22

so that means "5 gallons of Ginger ale and 22 gallons of cranberry juice can be bought in $120 so that no money is left over".

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y-intercept:

plug x=0 in above model

y=-(2/5)*x+24=-(2/5)*0+24=24

so y-intercept =24 means only 24 gallons of cranberry juice can be bought in $120 so that no money is left over.

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x-intercept:

plug y=0 in above model

0=-(2/5)*x+24

2/5x=24

x=60

so x-intercept =60 means only 60 gallons of Ginger ale can be bought in $120 so that no money is left over.

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