Answer:
There are 1,360 pears.
Step-by-step explanation:
Suppose that there are P pears and A apples.
We know that:
"If 20 apples and 60 pears are sold every hour, there will be 80 pears when all the apples are sold."
Suppose that all of these are sold after N hours, then:
20*N = A
80*N = P - 80
We also know that:
"if 60 apples and 20 pears are sold every hour, there will be 400 pears when all the apples are sold."
60*N = A
20*N = P - 400
Then we have four equations:
20*N = A
80*N = P - 80
60*N = A
20*N = P - 400
From the first one and the second one, we get:
20*N = A = 20*N = P - 400
A = P - 400
Now we have 3 equations:
80*N = P - 80
60*N = A
A = P - 400
Now we can just replace the third equation into the second one, then we get:
60*N = A = P - 400
Now we have two equations:
80*N = P - 80
60*N = P - 400
Now, remember that we want to find the number of pears, so we want to find the value of P.
To do it, we can take the quotient of the two equations, so we get:
(80*N)/(60*N) = (P - 80)/(P - 400)
8/6 = (P - 80)/(P - 400)
Now we can solve this for P
(8/6)*(P - 400) = P - 80
(8/6)*P - (8/6)*400 = P - 80
(8/6)*P - P = (8/6)*400 - 80
(2/6)*P = (8/6)*400 - 80
P = (6/2)*( (8/6)*400 - 80 )
P = 3*( (8/6)*400 - 80 ) = 1,360
There are 1,360 pears.
