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Question 1189317: Mia has a certain amount of money. If she buys 4 pens and 1 pencil, she will have $5 left over. If she buys 2 pens and 2 pencils, she will have $3 left over. If Edward arrives with the same amount of money as Mia, together they can buy 7 pens and 4 pencils and spend all their money. If a is the cost of one pen and b is the cost of one pencil, compute the ordered pair (a,b).
Answer by greenestamps(13215)   (Show Source):
You can put this solution on YOUR website!
When Mia buys 4 pens and 1 pencil, she has $5 left; the number of dollars she starts with is 4a+b+5.
When she buys 2 pens and 2 pencils, she has $3 left; the number of dollars she starts with is 2a+2b+3.
Since those two expressions represent the same number, set them equal to each other and simplify to get an equation in a and b.
4a+b+5=2a+2b+3
2a-b=-2 [1]
If Edward arrives with the same number of dollars that Mia started with, they can buy 7 pens and 4 pencils with all their money.
The total amount of money the two of them have is twice what Mia started with; and with that amount of money they can buy 7 pens and 4 pencils with no money left. Write an equation that says that and simplify to get a second equation in a and b.
8a+2b+10=7a+4b
a-2b=-10 [2]
Solve the pair of equations [1] and [2] by your favorite method.
I'll let you choose the method to use and work the problem to find the answer.
(Note: you should end up with the probably unreasonable answer that each pen costs $2 and each pencil costs $6....)
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