Ratio and Cross Multiplication
George had 121 sweets and Emmy had 328 sweets.After they gave away the same number of sweets, the ratio of George to Emmy became 1:4. Find the total number of sweets both of them gave away.
The ratio of the number of sweets with George and Emmy after they gave an equal number of them away was 1:4. We can denote the number of sweets with George as x and those with Emmy as 4x.
Let us denote the number of sweets they gave away as y.
This gives x + y = 121 and 4x + y = 328
3x = 207
=> x = 69
y = 121 - 69 = 52
Each of them gave away 52 sweets. The total number of sweets they gave away was 104.
The total number of sweets they gave away was 104.
Let' note the number of sweets given away by both of them as x.
George gave away 121 - x sweets and Emmy gave away 328 - x sweets.
After this, the ratio obtained is:
(121 - x)/(328 - x) = 1/4
We'll cross multiply and we'll get:
4*(121 - x) = 328 - x
We'll remove the brackets:
484 - 4x = 328 - x
We'll shift 4x to the right:
484 = 4x + 328 - x
We'll combine like terms:
484 = 3x + 328
We'll isolate 3x to the right:
484 - 328 = 3x
3x = 156
x = 52
The total number of sweets given away by both of them is x + x = 52+52 = 104 sweets.