document.write( "Question 101002: I really do want to be able to understand how to understand and be able to write this equations. I have tried on my own and nothing, plus I also need to be able to also solve the problem.\r
\n" ); document.write( "\n" ); document.write( "I have twice as many nickels as quarters. If the coins are worth $4.90, how many quarters and nickels do I have? \n" ); document.write( "
Algebra.Com's Answer #73517 by bucky(2189)\"\" \"About 
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You are dealing with unknown numbers of nickels and quarters. To help keep clear what is what,
\n" ); document.write( "let's use N to represent the number of nickels and Q to represent the number of quarters.
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\n" ); document.write( "The problem tells you that you have twice as many nickels as quarters. That means that the
\n" ); document.write( "number of nickels is twice the number of quarters. In equation form this becomes:
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\n" ); document.write( "N = 2*Q
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\n" ); document.write( "Next we know that a nickel is 5 cents. So for every nickel you have 5 pennies. The total
\n" ); document.write( "number of pennies you have in nickels can be found by multiplying the number of nickels N
\n" ); document.write( "by 5. So in pennies from nickels we have 5*N pennies.
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\n" ); document.write( "Similarly, we know that a quarter is 25 cents. So for every quarter you have 25 pennies. That
\n" ); document.write( "means that the total number of pennies you have from quarters can be found by multiplying
\n" ); document.write( "the number of quarters Q by 25. So from quarters we have 25*Q pennies.
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\n" ); document.write( "Finally we know that $4.90 is 490 pennies.
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\n" ); document.write( "So if we add the pennies from nickels to the pennies from quarters, the answer should be
\n" ); document.write( "490 pennies. In equation form this is:
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\n" ); document.write( "5N + 25Q = 490
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\n" ); document.write( "But earlier we said that N = 2Q. So in the \"pennies\" equation we can substitute 2Q for N
\n" ); document.write( "and when we do the pennies equation becomes:
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\n" ); document.write( "5(2Q) + 25Q = 490
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\n" ); document.write( "Multiply the 5*(2Q) to get 10Q and the equation reduces to:
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\n" ); document.write( "10Q + 25Q = 490
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\n" ); document.write( "Add the two terms on the left side of this equation to get:
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\n" ); document.write( "35Q = 490
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\n" ); document.write( "and finally, solve for Q by dividing both sides of this equation by 35 to get:
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\n" ); document.write( "Q = 490/35 = 14
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\n" ); document.write( "We now know that there are 14 quarters. And since there are twice as many nickels as
\n" ); document.write( "there are quarters, there must be 28 nickels.
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\n" ); document.write( "Let's check that. 28 nickels at 5 cents per nickel gives 28*5 = 140 pennies which is $1.40.
\n" ); document.write( "And 14 quarters at 25 cents each gives 14*25 = 350 pennies or $3.50. Added together
\n" ); document.write( "these two amounts are $1.40 + $3.50 = $4.90. That's what it is supposed to be so our answer
\n" ); document.write( "is correct.
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\n" ); document.write( "Hope this helps you to understand the problem a little better.
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