Socrates - Comenius 1: 
School Project “We are all living under the same sky”


Mathematics

Fifth task

Two colleagues decided to divide the fee for the shared work in the ratio 2 : 3. After they did so, they went together to dinner for which each of them paid 100 CZK. The remaining sums from the fee were in the ratio 3 : 5. How much was their shared fee?


Solution:

We describe: the first colleague got 2x CZK and the second colleague 3x CZK (the ratio 2 : 3). Each of them paid for the dinner 100 CZK. This way the ratio changed to 3 : 5.

The first colleague gets 2x – 100 CZK, the second colleague 3x – 100 CZK, but in the new ratio 3 : 5. That is why we work up the equation for calculation of one part of the fee:

One part is 200 CZK, then. The first colleague gets 2 . 200 CZK = 400 CZK, the second one 600 CZK = 3 . 200 CZK. Therefore the shared fee was 1000 CZK.