SOLUTION: Could any one help me with this system of linear equation as a word problem. Thank you in advance for your help. A shopper buys three oranges and five lemons for $10.26, while

Question 142967: Could any one help me with this system of linear equation as a word problem. Thank you in advance for your help.
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?
Answer by Earlsdon(6294) (Show Source): You can put this solution on YOUR website!
Let (O) = the price of one orange and (L) = the price of one lemon. From the problem description, you can write the two equations:
1) 3(O) + 5(L) = $10.26 "A shopper buys 3 oranges 3(O) and 5 lemons 5(L) for $10.26,..."
2) 6(O) + 4(L) = $11.16 "...a second shopper buys 4 lemons 4(L)and 6 oranges 6(O) for $11.16."
To solve this system of equations, first multiply equation 1) by 2 then subtract equation 2) from equation 1a) so that you can eliminate the variable (O).
1a) 2(3(O)+5(L) = $10.26)
1a) 6(O)+10(L) = $20.52
2) -(6(O) + 4(L) = $11.16) Subtract equation 2) from equation 1a)
--------------------------
6(L) = $9.36 Divide both sides by 6.
(L) = $1.56 This is the price of one lemon.
Substitute L = $1.56 into equation 1) and solve for (O).
1) 3(O) + 5($1.56) = $10.26 Simplify and solve for (O).
3(O) + $7.80 = $10.26 Subtract $7.80 from both sides.
3(O) = $2.46 Divide both sides by 3.
(O) = $0.82 This is the price of one orange.

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