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

Question 60861: 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 jai_kos(139) (Show Source): You can put this solution on YOUR website!
Let the cost of the chocolate bar = �x�
The cost of the pack of the gum = �y�
Sally bought 3 chocolate bars and a pack of gum = $1.75
3(chocolate bars) +(pack of a gum)= $1.75
3x + y = $1.75 (1)
Jake bought two chocolate bars and 4 packs of gum =$2.00
2(chocolate bars) + 4 ( packs of a gum) = $2.00
2x + 4y = 2.00 (2)

Solving the simultaneous equation, we get
3x + y = 1. 75
2x + 4y = 2.00
Now multiply equation(1) by 4,
3x * 4 + y * 4 = 1. 75 * 4
2x + 4y = 2.00
We get,
12x + 4 y = 7 (3)
2x + 4y = 2 (2)
Subtract the two equations, we get
10x = 5
x = (5/10)
x = (1/2) = 0 .5
Now we shall find the value of �y� by substituting the value of �x� in equation(2), we get
2(1/2) + 4 y = 2
1 + 4y = 2
4y = 2 -1
4y = 1
y = (1/4) = 0.25
Therefore the value of �x� is 0.5 and value of y is 0.25.
That is
The cost of chocolate bar = $0.5
The cost of the pack of gum = $0.25

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