SOLUTION: Sally brought three chocolate bars and a pack of gum and paid $1.75. Jake brought two chocolate bars and four packs of gum and paid $2.00. Find the cost of a chocolate bar and the
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Question 46398: Sally brought three chocolate bars and a pack of gum and paid $1.75. Jake brought 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?
Thank you. I have gotten so far as x = chocolate bar and y = gum. Found 2 solutions by tutorcecilia, saltzy57:Answer by tutorcecilia(2152) (Show Source):
You can put this solution on YOUR website! This is a systems of equations because there are two linear conditions:
3candy + 1 gum = $1.75 [First condition]
2candy + 4 gum = $2.00 [Second condition]
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3C + 1G = 1.75 [Solve using any type of method elimination, substituion, etc.]
2C + 4G = 2.00
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3C + 1G = 1.75 [Try the elimination method]
2C + 4G = 2.00
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-2(3C + 1G = 1.75) [Multiply through with -2 to eliminate the "C" term
+3(2C + 4G = 2.00) [Multiply through with 3 to eliminate the "C" term]
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-6C -2G = -3.50 [Multiply through with -2 to eliminate the "C" term]
+6C +12G = 6.00 [Multiply through with 3 to eliminate the "C" term]
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-6C -2G = -3.50 [Perform the indicated operations]
+6C +12G = 6.00
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0C +10G = 2.50
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10G = 2.50 [Solve for "G"]
G = 2.50/10
Gum = .25 cents each
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2C + 4(.25) = 2.00 [Plug-in G=.227 into either original equation]
2C + 1.00 = 2.00 [Solve for "C"]
2C + 1.00 - 1.00 = 2.00 - 1.00 [Simplify]
2C = 1.00
2C/2=1.00/2
Candy=0.50 cents each
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3C + 1G = 1.75 [Plug-in C=0.50 and G=.25 into the orginal equations]
3(0.50)+1(.25)=1.75[Plug-in C=0.50 and G=.25 into the orginal equations]
1.75=1.75 [Checks out]
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2C + 4G = 2.00 [Plug-in C=0.50 and G=.25 into the orginal equations]
2(0.50) + 4(.25) = 2.00
1.00 + 1.00=2.00
2.00=2.00 [checks out]
You can put this solution on YOUR website! 3x + 1y =1.75
2x + 4y =2.00
To find the cost of the choclate bar we must eliminate the gum from our equation.
One way to do that is to Multiply the first equation by 4 and substract the two equations
4(3x+Y)= 1.75
12x +4y = 7.00 now substract the 2nd equation from first
- 2x +4y = 2.00 you get the following equation
10x= 5.00 solve for x by dividing both sides by 10
x=.50
solve for y by plugging in value for x in either equation.
2*(.5) + 4*y = 2.00
1.00+4y=2.00
4y=1.00
y=.25
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