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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?

Aug 16, 2021

#1
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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.

Aug 16, 2021
#2
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florianmanteyw  Aug 16, 2021
#3
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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

Aug 24, 2021