James has a certain amount of money. If he buys 3 pens and 2 pencils, he will have $2 left over. If he buys 2 pens and 3 pencils, he will have $6 left over. If Judith arrives with the same amount of money as James, together they can buy 6 of each 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) .

isthebest123
Sep 4, 2018

#1**+1 **

The total amount of money James has is 3a + 2b + 2 = 2a + 3b + 6

Set these equations equal

3a + 2b + 2 = 2a + 3b + 6 rearrange as

a - b = 4

a = 4 + b

If Judith arrives with the same amount of money as James....then twice their money = 6 items each

2 ( 3a + 2b + 2) = 6a + 6b simplify

6a + 4b + 4 = 6a + 6b subtract 6a from both sides

4b + 4 = 6b subtract 4b from both sides

4 = 2b divide both sids by 2

2 = b ⇒ the pencils cost $2

And the pens cost a = 4 + b = 4 + 2 = $6

So (a,b) = (6, 2)

CPhill
Sep 4, 2018