Question 593730: I am just re-learning algebra after 20 years, so it's been difficult.
A college student earned $7300 during summer vacation working as a waiter in a popular restaurant. The student invested part of the money at 7% and the rest at 6%. If the student received a total of $458 in interest at the end of the yera, how much was invested at 7%?
Thank you.
Found 2 solutions by mananth, bucky:
Answer by mananth(16946)   (Show Source):
You can put this solution on YOUR website! Part I 7.00% per annum ---x
Part II 6.00% per annum ---y
Sum of their investments
x +y= 7300 -------------------1
Interest from both investments
7.00% x + 6.00% y= 458
Multiply by 100
7 x + 6 y= 45800.00 --------2
Multiply (1) by -7
we get
-7 x -7 y= -51100.00
Add this to (2)
0 x -1 y= -5300
divide by -1
y = 5300
Part I 6.00% $ 5300
Part II 7.00% $ 2000
CHECK
5300 --------- 6.00% ------- 318.00
2000 ------------- 7.00% ------- 140.00
Total -------------- 458.00
m.ananth@hotmail.ca
Answer by bucky(2189)  (Show Source):
You can put this solution on YOUR website! You have two unknowns, the amount of money invested at 7% (let's call that amount X) and the amount of money invested at 6% (let's call that amount Y). With two unknowns you will need two equations to find the two amounts.
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Since X plus Y equals the total money invested (which the problem says is $7300) we can write one equation (the first) as:
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X + Y = 7300
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Next, we can see that when the amount X is invested at 7% the amount of interest it will make in a year can be found by multiplying X times 0.07 (the decimal equivalent of 7%). Similarly when the amount Y is invested at 6% the amount of interest it will make in a year can be found by multiplying Y times 0.06. The problem tells you that if you add these two amounts of interest, the total interest will be $458. We can, therefore, write the equation for this. Our second equation is:
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0.07X + 0.06Y = 458
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We can, for convenience, get rid of the decimals in this second equation by multiplying both sides of the equation (all terms) by 100. In doing that we convert the equation to:
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7X + 6Y = 45800
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In summary, our two equations are:
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X + Y = 7300 and
7X + 6Y = 45800
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There are several ways we could solve this system of two equations. One of the ways would be to solve our first equation for Y in terms of X by subtracting X from both sides to get Y = 7300 - X. Then we could substitute 7300 - X for its equivalent value of Y in the second equation. This makes the second equation become:
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7X + 6(7300 - X) = 45800
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Do the distributed multiplication by multiplying 6 times each of the terms in the parentheses to make the equation become:
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7X + 43800 - 6X = 45800
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Combine the terms involving X by subtracting the 6X from the 7X to get just X which simplifies the equation to:
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X + 43800 = 45800
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Finally solve for X by subtracting the 43800 from both sides to get:
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X = 2000
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This says that X (the amount invested at 7% is equal to $2,000). That means that the remainder of the $7300 ... namely $5,300 ... is invested at 6%.
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Check by multiplying 7% times 2000 and 6% by 5300 to see if they total $458 dollars. 7% times $2000 is $140 and 6% times $5300 is $318. Add the two together to find that $140 + $318 = $458, just as the problem said it should.
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Another way you could have done it is to start with the two equations:
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X + Y = 7300 and
7X + 6Y = 45800
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Let's multiply the top equation by 6 (all terms on both sides) to make the top equation become 6X + 6Y = 43800. This with the second equation can be written as:
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6X + 6Y = 43800 and
7X + 6Y = 45800
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Subtract these two equations in vertical columns. Note that the 6X minus 6X in the second column equals zero and therefore disappears. The other subtractions result in:
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-X = -2000
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and multiply both sides by -1 to convert this equation to:
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X = 2000
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This is the same answer we got previously. It's just another way of doing it.
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Hope this helps you to understand the problem a little better. Good luck with your efforts to recall algebra. Use this site to help you. Maybe we'll hook up again.
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