Andrew and Cutter were assigned to buy refreshments for the History Club meeting

Question

Andrew and Cutter were assigned to buy refreshments for the History Club meeting. They bought the same items in the following amounts: Andrew: 3 six-packs of drinks, 2 bags of chips, and 4 packages of cookies, for a total cost of $22.00. Cutter: 2 six-packs of drinks, 4 bags of chips, and 5 packages of cookies, for a total cost of $26.30. After the meeting, Madeline agreed to buy the unused items at the purchase cost. She got 1 six-pack of drinks, 2 bags of chips, and 4 packages of cookies, for a total cost of $17.20. Find the cost of each item.

Explanation / Answer

Solution: Let price of six pack drinks = x,

price of bags of chips = y and

price of packages of cookies = z

now according to the problem the equations are

3x+2y+4z=22---- 1

2x+4y+5z=26.30 ------2

and

x+2y+4z=17.20 -------3

Now subtracting 3 from 1

i.e. 3x+2y+4z-(x+2y+4z) = 22-17.20

3x+2y+4z-x-2y-4z = 4.8

2x = 4.8

x = 2.4

now put x = 2.4 in equation 1 and 2

so equation 1 - -> 3x+2y+4z = 22

3(2.4)+2y+4z = 22

7.2+2y+4z = 22

2y + 4z = 14.8 ---4

For equation 2 - ->

2x+4y+5z=26.30

4.8+4y+5z=26.30

4y+5z=21.5---5

multiply equation 4 with number 2 we get

2(2y+4z) = 59.2

4y+8z = 29.6--6

Subtract 5 from 6

4y+8z-4y-5z=8.1

3z=8.1

z=2.7

Put this value in 5

we get

4y+5z=21.5

4y+5(2.7) = 21.5

4y+13.5=21.5

4y=8

y=2.

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