SOLUTION: Sally bought 3 chocolate bars and a pack of gum and paid $1.75. Jake bought 2 chocolate bars and 4 packs of gum and paid $2.00. Find the cost of a chocolate bar and the cost of a

Algebra ->  Conversion and Units of Measurement -> SOLUTION: Sally bought 3 chocolate bars and a pack of gum and paid $1.75. Jake bought 2 chocolate bars and 4 packs of gum and paid $2.00. Find the cost of a chocolate bar and the cost of a      Log On


   

Question 52216: Sally bought 3 chocolate bars and a pack of gum and paid $1.75. Jake bought 2 chocolate bars and 4 packs of gum and paid $2.00. Find the cost of a chocolate bar and the cost of a pack of gum.
Answer by tutorcecilia(2152) About Me  (Show Source):
You can put this solution on YOUR website!
3 choco. + 1 gum = $1.75
2 choco. + 4 guns = $2.00
.
Re-writing:
3x + 1y = 1.75
2x + 4y = 2.00
Solve using any method for solving a system of equations.
.
Using the method of elimination to solve:
-2(3x + 1y = 1.75)
+3(2x + 4y = 2.00)
____________________
.
.
-6x-2y=-3.5
+6x+12y=6
____________________
0x+10y=2.5
.
10y=2.5 [Solve for y]
y=.25 cents per gum
.
Plug y=.25 back into either of the original equations
3x + 1(.25) = 1.75 [Solve for x]
3x+.25=1.75
x=.50 cents per chocolate bar.
.
.
Checking:
3x + 1y = 1.75 [Plug-in x=.50 and y=.25]
3(.50) + 1(.25) = 1.75
1.75=1.75 [Checks out]
.
Checking
2x + 4y = 2.00 [Plug-in x=.50 and y=.25]
2(.50)+4(.25)=2.00
2=2 [checks out]
.

.