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# need this quick

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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) .

Sep 4, 2018

#1
+100587
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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)

Sep 4, 2018
#2
+67
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thx CPhill

:)

Sep 5, 2018