Question 249989
A = cost of an apple
O = cost of an orange
B = cost of a banana
.
The apple costs the same as 2 oranges...
A = 2*O
or
O = A/2
.
An orange and a banana costs 10 cents more than an apple...
A + 10 = O + B
so
A = O + B - 10
and
O = A + 10 - B
and
B = A + 10 - O
.
Two oranges cost 15 cents more than a banana
2*O = B + 15
so
O = (B+15)/2
and
B = 2*O - 15
.
Now we solve these equations.
The key strategy is to get all of the costs in terms of the same fruit...
Since we have 3 equations that can be defined in terms of O, we can start with that.
.
O = A/2
O = A + 10 - B
O = (B+15)/2
.
If a=b and b=c, then a=c.  So we know:
A/2 = A+10 - B
A = 2A + 20 - 2B
2B = A + 20
. 
A/2 = (B+15)/2
A = B+15
B = A - 15
2B = 2A - 30
.
A+20 = 2A - 30
.
A = 50
.
Using A = 50 cents, we are able to find the other values by substituting back into the original equations.
.
A = 2*O
so
O = 25
.
B = A + 10 - O
B = 50 + 10 - 25
B = 35
.
Substituting back into the initial equations, we are able to check these values.
.
The apple costs the same as 2 oranges...
This statement was used to calculate the value of the oranges, so of course it checks.
.
An orange and a banana costs 10 cents more than an apple...
O + B = 25 + 35 = 60
That is 10 cents more than an apple, so it checks.
.
Two oranges cost 15 cents more than a banana
2*25 = 50, which is 15 cents more than a banaa.
.
These all check.
So we can conclude that in this case:
Apples cost 50 cents.
Oranges cost 25 cents.
Bananas cost 35 cents.
,
Done