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Question 214685: The cost of 12 oranges and 7 apples is $5.36. Eight oranges and 5 apples cost $3.68. Find the cost of each orange
Sam invested a total of $10,000, part at 8% and the rest at 3%. How much was invested at 8% if he earned a total of $600 in one year? (Use the formula , Interest = principal * time * rate)
In an office there was a small cash box. One day Jane took half of the money plus $1 more. Then Mike took half of the remaining money plus $1 more. Rob then took the remaining $6. How many dollars were originally in the box?
The sum of two numbers is 8 less than twice the first number. Their difference is 4 less than twice the second number. What is the larger number?
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. Eight oranges and 5 apples cost $3.68. Find the cost of each orange
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Equations:
12r + 7a = 536 cents
8r + 5a = 368 cents
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Get rid of the "a's":
Multiply 1st Eq. by 5 and 2nd Eq. by 7 to get:
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60r + 35a = 5*536
56r + 35a = 7*368
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Subtract the 2nd from the 1st and solve for "r":
4r = 104
r = 26 cents (cost of one orange)
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Sam invested a total of $10,000, part at 8% and the rest at 3%. How much was invested at 8% if he earned a total of $600 in one year? (Use the formula , Interest = principal * time * rate)
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Interest + interest = interest
0.08x + 0.03(10000-x) = 600
Multiply thru by 100 to get:
8x + 30000 - 3x = 60000
5x = 30000
x = 6000 (amt invested at 8%)
4000 (amt invested at 3%)
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In an office there was a small cash box. One day Jane took half of the money plus $1 more. Then Mike took half of the remaining money plus $1 more. Rob then took the remaining $6. How many dollars were originally in the box?
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Start : x
After Jane: x -(1/2)x-1 = (1/2)x -1
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After Mike: [(1/2)x-1] - [(1/2)x-1]/2 -1 = (1/2)[(1/2)x-1]-1
= (1/4)x - (3/2)
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Equation:
(1/4)x - (3/2) = 6
(1/4)x = 7.5
x = 30
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Checking:
30 -(15+1) = 14
14-(7+1) = 6
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OK
Original amount = $30
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The sum of two numbers is 8 less than twice the first number. Their difference is 4 less than twice the second number. What is the larger number?
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Equations:
a + b = 2a-8
a - b = 2b-4
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Rearrange:
a = b + 8
a = 3b-4
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Substitute to get:
b+8 = 3b-4
2b = 12
b = 6
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Substitute into a = b+8 to get:
a = 14
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Cheers,
Stan H.
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