SOLUTION: I am horrible at word problems and could really use some help. My problem reads: Sally bought three chocolate bars and a pack of gum and paid $1.75. Jake bought two chocolate bars

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Question 121088: I am horrible at word problems and could really use some help. My problem reads: 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. Find the cost of a chocolate bar and the cost of a pack of gum. Thanks!
Answer by nabla(475) About Me  (Show Source):
You can put this solution on YOUR website!
Let chocolate bars=x, and gum=y. You can now form the following system of equations and solve via a few methods, here I will show you how to use row operations (you could more easily just use substitution, but I will leave that up to you):
3x%2By=1.75
2x%2B4y=2
Simplify the second equation by dividing both sides by 2:
3x%2By=1.75
x%2B2y=1
Take 1/3 the first equation:
x%2B%281%2F3%29y=1.75%2F3
x%2B2y=1
Subtract the first equation from the second equation:
x%2B%281%2F3%29y=1.75%2F3
%285%2F3%29y=1.25%2F3
We can now simplify for y:
x%2B%281%2F3%29y=1.75%2F3
y=1.25%2F5=.25=1%2F4
Now, subtract (1/3) of equation two from the first equation:
x=1.75%2F3-1%2F12=7%2F12-1%2F12=1%2F2
y=1%2F4
Giving us the solution set S={1/2,1/4}.
To check,
1. 3%2A1%2F2%2B1%2F4=7%2F4=1.75
2. 2%2A1%2F2%2B4%2A1%2F4=1%2B1=2
Note that the chocolate bars cost $0.50, and the packs of gum cost $0.25.
If you have further difficulty, E-mail me by going to my "me" page.