SOLUTION: OK, new problem. Sally bought three choclate bars and a pack of gum and paid $1.75. Jake bought two choclate bars and four packs of gum and paid $2.00. Find the cost of a choclat

Algebra ->  Customizable Word Problem Solvers  -> Misc -> SOLUTION: OK, new problem. Sally bought three choclate bars and a pack of gum and paid $1.75. Jake bought two choclate bars and four packs of gum and paid $2.00. Find the cost of a choclat      Log On

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Question 73402: OK, new problem.
Sally bought three choclate bars and a pack of gum and paid $1.75. Jake bought two choclate bars and four packs of gum and paid $2.00. Find the cost of a choclate bar and a pack of gum.
I think the format for this goes like this but I am not sure I am right. I would put the x/choclate bars and y/gum for each then work it out for each right? Help!!!
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Let c=price of chocolate bar, g=price of gum
The word problem translates to
3c%2Bg=1.75Sally bought three choclate bars and a pack of gum and paid $1.75
2c%2B4g=2Jake bought two choclate bars and four packs of gum and paid $2.00
Solve for g on the first equation
g=1.75-3cPlug this into g of 2c%2B4%2Ahighlight%28g%29=2
2c%2B4%2Ahighlight%281.75-3c%29=2Now distribute the 4
2c%2B7-12c=2Subtract like terms
-10c=2-7Subtract 7 from both sides
-10c=-5Divide both sides by -10
c=-5%2F-10
c=1%2F2
So the chocolate bar costs $0.50. Use this to find the price of gum
2%28.5%29%2B4g=2
1%2B4g=2
4g=1
g=1%2F4
So the gum costs $0.25
Check:
3c%2Bg=1.75
3%280.5%29%2B0.25=1.75
1.5%2B0.25=1.75
1.75=1.75Works
2c%2B4g=2
2%280.5%29%2B4%280.25%29=2
1%2B1=2
2=2Works