Question

There are two jars of sweets.

If 20 are taken from the first jar and put into the second, they are in the ratio of 1:2
If 60 are now taken from the second and put into the first, they are in the ratio of 3:1
Work out the original amount in each.

Answer 1

First, we model two equations that satisfy the problem. Let x be the number of sweets in the first jar, and y the number of sweets in the second jar.
First equation:
(x-20)/1 = (y+20)/2
or
(x-20)/(y+20) = 1/2

Second equation:
[(x-20)+60]/3 = [(y+20)-60]/1
or
(x+40) = 3(y-40)

Expressing the first equation in terms of y, we have:
y = 2x - 60

Plugging it in to the second equation:
(x+40) = 3[(2x-60) - 40]
5x = 340
x = 68

y = 2(68)-60 = 76

The first jar originally had 68 sweets and the second jar originally had 76 sweets.