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I have a pouch with pens and pencils in it. At the end of math class, the ratio of pens to pencils is 9:7. While walking from math class to photography class, I found three pens and one pencil. After I put them in my pouch, the ratio of pens to pencils was 7:5. How many pencils did I have at that point?

 Dec 9, 2018
 #1
avatar+98102 
+1

I have a pouch with pens and pencils in it. At the end of math class, the ratio of pens to pencils is 9:7. While walking from math class to photography class, I found three pens and one pencil. After I put them in my pouch, the ratio of pens to pencils was 7:5. How many pencils did I have at that point?

 

Call x the number of pens tha you had at first....and y the number of pencils you had at first

 

So....we now that

 

x / y =   9/7      which implies that  x = (9/7)y       (1)

 

 

Afteryou found three pens and one pencils we know that

 

[ x + 3] / [ y + 1]  =  7/5        cross-multiply

 

5[ x + 3 ] =  7 [ y + 1]

 

5x + 15  =   7y + 7           sub (1) in for x

 

5(9/7)y + 15 = 7y + 7      simplify

 

(45/7)y + 15 = 7y + 7

 

15 - 7  =   7y - (45/7)y

 

8 =  (49/7)y - (45/7)y

 

8 = (4/7)y 

 

6 (7/4) = y =   14   = no. of pencils initially

 

And you added one...so....now you have 15

 

Check

 

You had   (9/7)y = (9/7)(14) =  (9 )(14/7) = 9 * 2 = 18 pens originally

So    18/14  =  9/7

 

And at the end you had    [ 18 + 3] / [ 14 + 1]  =   21 / 15   =  7 / 5

 

 

cool cool cool

 Dec 9, 2018
 #2
avatar+17286 
+2

7/16 x  = pencils where  x = total number of writing instruments

 

7/ 16 x  + 1  = 5/12 (x+4)

21/48  x + 1 = 20/48 x + 80/48

1/48 x = 32/48

x = 32    pencils+ pens originally  

7/16 (32) = 14  pencils originally   ... and you found one more    = 15

 Dec 9, 2018
 #3
avatar+72 
0

7/16 x  = pencils where  x = total number of writing instruments

 

7/ 16 x  + 1  = 5/12 (x+4)

21/48  x + 1 = 20/48 x + 80/48

1/48 x = 32/48

x = 32    pencils+ pens originally  

7/16 (32) = 14  pencils originally   ... and you found one more    = 15

 Dec 9, 2018

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