+166 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?
+129899 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
+37153 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
