SOLUTION: Sally bought three chocolate bars and a pack of gum and paid $1.75. Jake bought two chocolate bars and four packs of gum and paid $2.00. What's the cost of a chocolate bar and a pa

Question 121815: Sally bought three chocolate bars and a pack of gum and paid $1.75. Jake bought two chocolate bars and four packs of gum and paid $2.00. What's the cost of a chocolate bar and a pack of gum?
Found 2 solutions by checkley71, solver91311:
Answer by checkley71(8403) (Show Source): You can put this solution on YOUR website!
3C+G=1.75 G=1.75-3C
2C+4G=2.00
2C+4(1.75-3C)=2.00
2C+7-12C=2.00
-10C=2-7
-10C=-5
C=-5/-10
C=.50 FOR THE COST OF A CHOCOLATE BAR.
3*.50+G=1.75
1.50+G=1.75
G=1.75-1.50
G=.25 FOR THE COST OF THE GUM.
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
Let's say that a chocolate bar costs 'c' cents, and a pack of gum costs 'g' cents.

Sally bought 3 chocolate bars, so she spent 3c cents on chocolate. Likewise, she spent 1g, or just g, cents on gum. Together she spent $1.75, or 175 cents. Now we can write:

A similar analysis gives us an expression for Jake's purchase:

Now we have a system of two linear equations in two variables. We are interested in determining the ordered pair (c,g) that satisfies both equations. This looks like a good candidate for the elimination method because the substitution expressions look a little messy to me. (This is a matter of personal preference, or perhaps the instructions in an assignment. Either way, properly performed gets you to the same place)

Multiply equation 1 by -4:

Add the result to the second equation:

Divide by -10

Now we know that chocolate bars cost 50 cents. Substitute this value into either original equation:

So gum costs 25 cents.

Finally, convert your answers back to dollars and cents notation because that was the form of the given values for money in this problem,
Chocolate Bars: $0.50
Gum: $0.25

Check the answer:

and

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