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The ratio of the number of pencils to the number of erasers in a box was 3 : 4 at first. After adding 12 pencils and removing 15 erasers from the box, the ratio of the number of pencils to the number of erasers became 1 : 1. How many erasers were there in the box at the end?

Aug 11, 2021

#1
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Given :

Intially ratio of pencil to eraser in a box = 3:4

After adding 12 pencils and removing 15 erasers it became 1:1.

To find :

How many eraser in the box ?

Given that the ratio of pencil to eraser is 3 : 4 .

If there is initially x pencils and y erasers ,

So, we can write

x/y = 3/4

Or y = 4x/3

And if we add 12 more pencils and remove 15 erasers then the ratio will be 1 : 1,

So, we can write

(x + 12) / (y - 15) = 1/1

x  + 12 = y - 15

Now, put the value of y

x + 12 = 4x/3 - 15

4x/3 - x = 15 + 12.

x/3 = 27

x = 81.

Now y will be

y = 4x/3

y = 108

But it is the Intial values of x and y.

The number of erasers at the end will be

= y - 15

= 108 - 15

= 93

The number of erasers in the box at the end is 93.

Aug 11, 2021
#2
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$p = \frac{3}{4} e$

$p + 12 = e - 15$

$p = e-27$

$\frac{3}{4}e = e - 27$

$\frac{1}{4}e = \frac{1}{3}e - 9$

$e = \frac{4}{3}e - 36$

$\frac{1}{3}e = 36$

$e = 108$

$e-15 = 108 \Rightarrow e = \boxed{93}$

Aug 11, 2021