SOLUTION: An apple costs the same as 2oranges. Together, an orange and a banana cost .10 more than an apple. Two oranges cost .15 more than a banana. what is the cost for one of each fruit?

Question 249989: An apple costs the same as 2oranges. Together, an orange and a banana cost .10 more than an apple. Two oranges cost .15 more than a banana. what is the cost for one of each fruit?
Found 2 solutions by ankor@dixie-net.com, oberobic:
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
An apple costs the same as 2oranges. Let g = no. or oranges
a = 2g
:
Together, an orange and a banana cost .10 more than an apple.
g + b = a + .10
b = a - g + .10
Replace a with 2g
b = 2g - g +.10
b = g + .10
:
Two oranges cost .15 more than a banana.
2g = b + .15
Replace b with (g+.10)
2g = (g+.10) + .15
2g = g + .25
2g - g = .25
g = .25, is the price of each orange
:
what is the cost for one of each fruit?
a = 2g
a = 2(.25)
a = .50, is the price of each apple
:
b = g + .10
b = .25 .10
b = .35, is the price of each banana
;
:
Check solution in the statement:
Together, an orange and a banana cost .10 more than an apple.
.25 + .35 = .50 + .10; confirms our solutions
Answer by oberobic(2304) (Show Source): You can put this solution on YOUR website!
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
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