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. Find the cost of a chocolate bar and the

Algebra ->  Graphs -> 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. Find the cost of a chocolate bar and the       Log On


   

Question 112042: 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.
Answer by BrittanyM(80) About Me  (Show Source):
You can put this solution on YOUR website!
We can use a system of equations in order to solve for the variables.
Sally bought three chocolates and one pack of gum for 1.75
So:
3C + 1G = 1.75
And Jake bought two chocolates and four packs of gum for 2.00
So:
2C + 4G = 2.00

3C + 1G = 1.75
2C + 4G = 2.00

From the top equation, we can subtract 3C in order to find the value of 1G in terms of C.

1G = -3C + 1.75

Now, we can plug this into the other equation to find the exat value of C.

2C + 4(-3C + 1.75) = 2.00
2C - 12C + 7 = 2.00
-10C = -5
C = 0.50

Now we can plug this value into either of the equations from the system so we can solve for G.

3(0.50) + 1G = 1.75
1.5 + 1G = 1.75
1G = 0.25

So one chocolate costs 0.50,
And one pack of gun costs 0.25.