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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
avatar+100587 
+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)

 

 

cool cool cool

 Sep 4, 2018
 #2
avatar+67 
+1

thx CPhill

:)

 Sep 5, 2018

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