At the beggining of the day some small eggs and some large eggs were on sale at the ratio 3:2. At the end of that day, 260 small eggs and 1/2 of the large eggs were sold. The ratio of the remaining small ones to the remainig large ones became 2:5. How many eggs were there at first?
Beginning eggs:
3/2=L/S or
3S=2L
End eggs:
2/5=(L-1/2L)/(S-260)
Two equations, two unknowns.
To solve this problem, we'll use a system of equations. Let's assign variables to represent the number of small eggs and large eggs at the beginning of the day.
Let's say the number of small eggs is 3x and the number of large eggs is 2x.
According to the problem, 260 small eggs were sold, so the number of remaining small eggs is 3x - 260.
Half of the large eggs were sold, so the number of remaining large eggs is 2x/2 = x.
The ratio of the remaining small ones to the remaining large ones became 2:5, so we can represent it as (3x - 260)/(x) = 2/5.
Now, we can solve this equation to find the value of x.
(3x - 260)/(x) = 2/5
Cross-multiplying, we get:
5(3x - 260) = 2(x)
15x - 1300 = 2x
Bringing like terms to one side:
15x - 2x = 1300
13x = 1300
Dividing both sides by 13:
x = 100
Therefore, the number of large eggs at the beginning of the day is 2x = 2(100) = 200.
And the number of small eggs at the beginning of the day is 3x = 3(100) = 300.
In total, there were 300 small eggs and 200 large eggs at first.