+120 In the morning, the ratio of the chicken eggs to the quail eggs at the market was 3 : 2. By the evening, 210 chicken eggs were sold, the ratio of the number of chicken eggs to the quail eggs became 1 : 3. How many eggs were at the market in the end?
+63 Let me express this in algebra form.
Lets put Quail as Q, and Chicken as C.
3C=2Q
3C-210/2Q = 1/3
Lets bring 2Q into 3C.
2Q-210/2Q=1/3
We can use cross multiplication.
6Q-630=2Q
4Q=630
Q=157.5
2Q=315
There are 315 Quail eggs.
But, we want the total number of eggs at the end, so we must find the amount of chicken eggs too.
3C=2Q
3C=315
We want 3C-210.
315-210=105
So the total number of eggs is 105+315=420 eggs at the end.
+120 That's the WRONG answer. It's easy to get wrong answers but hard to get correct answers
C : Q = 3 : 2
C - 210 : Q = 1 : 3
\({C \over Q} = { 3 \over 2}\)
\({{C - 210} \over Q} = { 1 \over 3}\)
so C = (3/2)Q
\({{{3 \over 2}Q - 210} \over Q} = {1 \over 3}\)
\({{3 \over 2}Q} - 210 = {1 \over 3}Q\)
\({3 \over 2} - {1 \over 3} = {9 \over 6} - {2 \over 6} = {7 \over 6}\)
\({7 \over 6}Q = 210\)
so Q = 180
So C = 270
now C = 60
so a total of 240
