Question 178493: The cost of 12 oranges and 7 apples is $5.36. 8 oranges and 5 apples cost $3.68. what is the cost of each orange? Found 3 solutions by stanbon, Mathtut, josmiceli:Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website! The cost of 12 oranges and 7 apples is $5.36. 8 oranges and 5 apples cost $3.68. what is the cost of each orange?
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Value Equation: 12R + 7A = 536 cents
Value Equation: 8R + 5A = 368 cents
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Multiply thru the 1st equation by 2; Multiply thru the 2nd equation by 3:
24R + 14A = 1072
24R + 15A = 1104
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Subtract 1st from 2nd to get:
A = 32 (price of an apple)
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Substitute to solve for "R":
8R + 5*32 = 368
8R + 160 = 368
8R = 208
R = 26 (price of an orange)
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Cheers,
Stan H.
You can put this solution on YOUR website! let the cost of each apple and orange be a and o respectively
:
7a+12o=5.36...eq 1
5a+8o=3.68....eq 2
:
use elimination method. muliply all terms in eq 1 by -5 and all terms in eq 2 by 7
:
-5(7a+12o=5.36--->-35a-60o=-26.8.....eq 1 revised
7(5a+8o=3.68------>35a+56o=25.76.....eq 2 revised
:
It is plain to see that the a terms are eliminated when you add these two equations together because -35a+35a=0. We are left with -60o+56o=-26.8+25.76
:
-4o=-1.04
: cents-cost of an orange
:
take o's found value and plug it back into any numbered equation
:
I choose eq 2
:
5a+8(.26)=3.68
:
5a+2.08=3.68
:
5a=1.60
: cents-cost of an apple
:
You can put this solution on YOUR website! Let = the cost of 1 orange in cents
Let = the cost of 1 apple in cents
Given:
(1)
(2)
Multiply both sides of (1) by
Multiply both sides of (2) by
Then subtract (2) from (1)
(1)
(2)
The cost of each orange is $.26
check:
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OK
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