document.write( "Question 1160362: A boy has $3.70 in dimes and quarters. If the dimes were quarters, and the quarters were dimes, the money would have been $4.00. How many coins does the boy have? \n" ); document.write( "

Algebra.Com's Answer #783647 by ikleyn(52782) $\"\"$ $\"About$

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\n" ); document.write( "A boy has $3.70 in dimes and quarters. If the dimes were quarters, and the quarters were dimes,
\n" ); document.write( "the money would have been $4.00. How many coins does the boy have?
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document.write( "From the condition, you have these two equations\r\n" );
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document.write( "    10d + 25q = 370       (1)\r\n" );
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document.write( "    25d + 10q = 400       (2)\r\n" );
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document.write( "Multiply equation (1) by 5 (both sides). Multiply equation (2) by 2  (both sides)\r\n" );
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document.write( "     50d +  125q = 1850    (3)\r\n" );
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document.write( "     50d +   20q =  800    (4)\r\n" );
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document.write( "Subtract equation (4) from equation (2)\r\n" );
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document.write( "           105q = 1850 - 800 = 1050.\r\n" );
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document.write( "             q            = 1050/105 = 10.\r\n" );
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document.write( "Then from equation (1),  d = (370-25*10)/10 = 12\r\n" );
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\n" ); document.write( "\n" ); document.write( "ANSWER. There are 12 dimes and 10 quarters. The total number of coins is 22.\r
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\n" ); document.write( "\n" ); document.write( "Another way to find the total number of coins is to add equations (1) and (2).\r
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document.write( "You will get then\r\n" );
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document.write( "    35d + 35q  = 370 + 400\r\n" );
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document.write( "    35*(d + q) = 770\r\n" );
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document.write( "    d + q =  = 22.\r\n" );
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