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?

grif389 Dec 9, 2018

#1**+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

CPhill Dec 9, 2018

#2**+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

ElectricPavlov Dec 9, 2018