SOLUTION: Help!! Someone I am having trouble with word problem, by turning this into an algebraic equation in order to solve it: A shopper buys three oranges and five lemons for $10.26, whi

Question 142979: Help!! Someone I am having trouble with word problem, by turning this into an algebraic equation in order to solve it:
A shopper buys three oranges and five lemons for $10.26, while a second shopper buys four lemons and six oranges for $11.16. What is the price of each fruit? If i'm not mistaken, you have to solve for each shopper and then divide. Am i right? Thank you in advance.
Found 2 solutions by stanbon, BrittanyM:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
A shopper buys three oranges and five lemons for $10.26, while a second shopper buys four lemons and six oranges for $11.16. What is the price of each fruit?
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Let the price of oranges be "r"; Let the price of lemons be "m".
------------
EQUATIONS:
3r + 5m = 10.26
6r + 4m = 11.16
--------------
Solve for any method to get
r = 0.82 = 82 cents (price of an orange)
m = $1.56 (price of a lemon)
==============
Cheers,
Stan H.
Answer by BrittanyM(80) (Show Source): You can put this solution on YOUR website!
The easiest way to solve this problem is to set up an equation to represent the products purchased and prices paid by each shopper. Then, we can solve for the individual prices of the products by using a system of equations.

Our equation of the first shopper is
3(O) + 5(L) = 10.26
where o is orange and l is lemon.

For the second shopper, we have
6(O) + 4(L) = 11.16

Now, we set these two equations up in a system and solve.

3(O) + 5(L) = 10.26
+ 6(O) + 4(L) = 11.16
--------------------
Because there are two separate variables, we must eliminate one before we can solve for the real values. We may do this by multiplying the entire top equation by negetive two. When combined with the bottom equation, it will eliminate the oranges so we can solve for lemons.

-2(3(O) + 5(L) = 10.26)
+ 6(O) + 4(L) = 11.16
--------------------

-6(O) -10(L) = -20.52
+ 6(O) + 4(L) = 11.16
--------------------
0(O) -6(L) = -9.36

-9.36/-6 = L

So the price of a lemon is 1.56

Now, since we know the price of one of our variables, we can plug it into either of the equations from the system in order to find the cost of an orange.

3(O) + 5(1.56) = 10.26
Solving for O, we get 0.82

In order to check our answers, we can plug them back into the equations and make wure that the resulting statement is true.

3(0.82) + 5(1.56) = 10.26
This is true, so our answers are validated.

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