document.write( "Question 53622: Nadine has seven more nickels than Delano has dimes. If Delano gives Nadine four of his dimes, then Delano will have the same amount of money as Nadine. How much money do they have together? (Assume that Nadine has only nickels and Delano has only dimes.) \n" ); document.write( "

Algebra.Com's Answer #35877 by aaaaaaaa(138) $\"\"$ $\"About$

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Nadine's nickels: n
\n" ); document.write( "Delano's dimes: d
\n" ); document.write( "Money that Nadine has: 5n
\n" ); document.write( "Money that Delano has: 10d\r
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\n" ); document.write( "\n" ); document.write( "n = d + 7
\n" ); document.write( "n - d = 7\r
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\n" ); document.write( "\n" ); document.write( "5n + 40 = 10(d-4)
\n" ); document.write( "5n + 40 = 10d - 40
\n" ); document.write( "5n - 10d = -80\r
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Solved by pluggable solver: SOLVE linear system by SUBSTITUTION

Solve:
\n" ); document.write( " $\"+system%28+%0D%0A++++1%5Cn+%2B+-1%5Cd+=+7%2C%0D%0A++++5%5Cn+%2B+-10%5Cd+=+-80+%29%0D%0A++\"$ We'll use substitution. After moving -1*d to the right, we get:
\n" ); document.write( " $\"1%2An+=+7+-+-1%2Ad\"$ , or $\"n+=+7%2F1+-+-1%2Ad%2F1\"$ . Substitute that
\n" ); document.write( " into another equation:
\n" ); document.write( " $\"5%2A%287%2F1+-+-1%2Ad%2F1%29+%2B+-10%5Cd+=+-80\"$ and simplify: So, we know that d=23. Since $\"n+=+7%2F1+-+-1%2Ad%2F1\"$ , n=30.
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\n" ); document.write( " Answer: $\"system%28+n=30%2C+d=23+%29\"$ .
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