SOLUTION: Mike has 2 more dimes than quarters and 7 more nickels than quarters. The total value of the coins is $1.75. How many quarters does he have? I tried doing two equations: 2(.1d)+.25

Question 504302: Mike has 2 more dimes than quarters and 7 more nickels than quarters. The total value of the coins is $1.75. How many quarters does he have? I tried doing two equations: 2(.1d)+.25q and 7(.5n)+.25q but that didn't work out too well because then, I didn't know how to get to 1.75.
Answer by bucky(2189) (Show Source): You can put this solution on YOUR website!
The common thread in this problem is that the number of coins of each type is expressed in terms of the number of quarters. So let's start by calling the number of quarters Q.
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Then the number of dimes is said to be 2 more than the number of quarters. In other words the number of dimes is Q+2.
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Finally, the number of nickels is 7 more than the number of quarters. So we can say that the number of nickels is Q+7.
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Then to avoid working with decimals, let's just use the number of cents for the value of each coin. Each dime is 10 cents, so we can find the number of cents in dimes by multiplying 10 times the number of dimes. In algebraic form this is 10 times the quantity Q+2 or 10(Q+2) cents.
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Similarly the number of cents for each nickel is 5 cents. There are Q+7 nickels so that the number of cents in nickels is 5(Q+7).
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Finally, there are 25 cents for each quarter. So the number of cents from quarters is 25 times the number of quarters or 25Q.
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We know that the total number of cents we have is 175 which is the same as $1.75.
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So we can add up the total number of cents from the three coins and set it equal to 175 as follows:
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10(Q+2) + 5(Q+7) + 25Q = 175
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Do the two distributive multiplications to get:
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10Q + 20 + 5Q + 35 + 25Q = 175
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On the left side collect the common terms (those containing Q and those that do not) and get:
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(10Q + 5Q + 25Q) + (20 + 35) = 175
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Add the terms in each of the two sets of parentheses:
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40Q + 55 = 175
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Subtract 55 from both sides and you have:
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40Q = 120
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Solve for Q by dividing both sides by 40 and the result is:
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Q = 120/40 = 3
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There are three quarters. Then we can backtrack to find that the number of dimes is 2 plus the number of quarters or 2 + 3. So there are 5 dimes. Finally we can determine the number of nickels because we know that there are 7 more nickels than quarters. Therefore, there are 7 + 3 = 10 nickels.
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Now check: Three quarters is 75 cents, 5 dimes is 50 cents and 10 nickels is also 50 cents. So we have 75 cents + 50 cents + 50 cents and that totals up to $1.75.
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Hope this helps you to understand the problem. The major clue was the fact that the number of coins of each type were all based on the number of quarters.

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