Question

Derrick, Eron and Foster shared the cost of renting their apartment. Derrick and Eron paid 2/3 of the cost. Eron and Foster paid 3/4 of the cost. Eron paid $450 more than Derrick. How much did they pay altogether?

Answer 1

D+E = 2x/3
E+F = 3x/4
E = D+45 ----> E - D = 450 , but E + D = 2x/3
so 2E = 450 + 2x/3
E = 225 + x/3 **

We know D+E+F = x , but E+F = 3x/4, so
D = x/4

in D+E = 2x/3, we know D = x/4 , so
x/4 + E = 2x/3
E = 2x/3 - x/4 = 5x/12

so we have E = E
5x/12 = 225 + x/3
5x/12 - x/3 = 225
x/12 = 225
x = 27,000 , YEAHH

then
D = x/4 = 675
E = 5x/12 = 1125
F = 27000 - D - E = 900

I will leave it up to you to check those values
e.g. is D+E = 2/3 of 27,000 ?
etc