SOLUTION: Please help: Sally bought three chocolate bars and a pack of gum and paid $1.75. Jake bought two chocolate bars and four packs of gum ans paid $2.00. Find the cost of a chocolate

Question 95040: Please help:
Sally bought three chocolate bars and a pack of gum and paid $1.75. Jake bought two chocolate bars and four packs of gum ans paid $2.00. Find the cost of a chocolate bar and the cost of a pack of gum.
Found 2 solutions by kiljoy, williacy:
Answer by kiljoy(51) (Show Source): You can put this solution on YOUR website!
If you don't have a specific method to solve this. We can solve it using the addition of equations.
We'll use c to represent a chocolate bar and g to represent the gum.

Take the equation times -4, the equation becomes...

Add to the other equation.

Now substitute our c value of .50 into either equation to solve for g.

This gives us, $.50 for the chocolate and $.25 for the gum.
To do a check, substitute both values into either equation.

Answer by williacy(2) (Show Source): You can put this solution on YOUR website!
Since the first unknown is the chocolate bars, let x = chocolate bars. The second unknown is the packs of gum, so let y = packs of gum.
3x + 1y = 1.75 - for Sally
2x + 4y = 2.00 - for Jake
Multiply the top equation by -4 so that the y values can be the inverse of one another.
-4(3x + 1y) = -4(1.75)
-12x + -4y = -7.00
Add : -12x + -4y = -7.00
2x + 4y = 2.00
-10x = -5.00 divide both sides by -10
x = -0.50
Now substitute the value of x into one of the original problems, and solve for y.
3(-0.50) + y = 1.75
-1.50 + y = 1.75
y = 0.25
Therefore x(chocolate bars) = $0.50 and y(packs of gum) = $0.25

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