Question 540329: chuck norris has $2.55 made up of pennies, and dimes and quarters. She has as many dimes aspennies and she has eighteen coins all. How many quarters does she have?
PLs. help me!..can you please show how to get the answer? thank u! pls..hel me!!
Answer by bucky(2189)   (Show Source):
You can put this solution on YOUR website! Let's work this problem in terms of cents. $2.55 is equal to 255 cents.
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Let's also say that P represents the unknown number of pennies, D represents the unknown number of dimes, and Q represents the unknown number of Quarters.
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Each penny equals 1 cent. Each dime equals 10 cents. Therefore, the total number of cents from dimes can be found by multiplying 10 times the number of dimes. This is written as 10D. Each quarter equals 25 cents. So we can find the total number of cents from quarters by multiplying 25 times the number of quarters. And this is written as 25Q. We can find the total number of cents by adding these amounts up as follows:
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P + 10D + 25Q
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And we know that the total number of cents equals 255. So one equation we can get from this problem is:
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P + 10D + 25Q = 255
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Next the problem tells us that the number of pennies is equal to the number of dimes. So we can write that P = D, and since P and D are equal we can substitute P in the place of D in the equation that totals up the number of cents. When we do that substitution we get:
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P + 10P + 25Q = 255
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Finally we are told that the total number of coins is 18. So let's add up the number of each type of coin and set it equal to 18 as follows:
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P + D + Q = 18
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Again we know that the number of pennies (P) equals the number of dimes (D). So we can replace D with P in the equation for the total number of coins. When we do that the equation becomes:
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P + P + Q = 18
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Add together the P + P to get 2P and the equation reduces to:
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2P + Q = 18
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Let's now solve this equation for Q by subtracting 2P from both sides to get:
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Q = 18 - 2P
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The reason that we did this is because now we can return to the equation:
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P + 10P + 25Q = 255
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And we can replace Q with its equal 18 - 2P. Doing that results in:
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P + 10P + 25(18 - 2P) = 255
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Do the distributed multiplication by multiplying 25 times each of the terms in the parentheses. 25 times 18 is 450 and 25 times -2P is -50P. So the equation is:
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P + 10P + 450 - 50P = 255
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We have now got an equation that has only 1 unknown. This should (with a little work) be solvable for the unknown P. Let's first add up all the terms on the left side that contain P. When we do we get P + 10P - 50P = -39P and the equation reduces to:
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-39P + 450 = 255
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We will now get rid of the 450 on the left side by subtracting 450 from both sides. On the left side the +450 and the subtracted 450 cancel each other out, making the 450 gone from that side. On the right side the 255 minus 450 becomes -195. So this simplified equation is:
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-39P = -195
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Solve for P by dividing both sides by -39. When we do that we get:
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P = (-195)/(-39) = 5
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This tells us that we have 5 pennies. And we know that the number of pennies equals the number of dimes. So we have 5 dimes. The number of pennies (5) and the number of dimes (5) add up to 10 coins. But we know there are 18 total coins. The only coins left are quarters. Since the pennies and dimes are 10 coins, then the number of quarters must be the remaining 8 coins.
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As a check of our answer (5 pennies, 5 dimes, and 8 quarters) let's add up to see what the total amount of money is. The 5 pennies is 5 cents. The 5 dimes is 50 cents because 5*10 = 50. And the 8 quarters is 200 cents because 25*8 = 200. When we add these amounts we get:
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5 + 50 + 200 = 255
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and this agrees with the amount that the problem tells us that it should be. So our answer checks: 5 pennies, 5 dimes, and 8 quarters.
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Hope this helps you to understand how to work this problem.
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