SOLUTION: I have a box of nickels and dimes. When I counted the money, I was surprised to see that I have exactly $10. Then it occurred to me that if my nickels were dimes and my dimes were

Algebra ->  Linear-equations -> SOLUTION: I have a box of nickels and dimes. When I counted the money, I was surprised to see that I have exactly $10. Then it occurred to me that if my nickels were dimes and my dimes were       Log On


   



Question 916434: I have a box of nickels and dimes. When I counted the money, I was surprised to see that I have exactly $10. Then it occurred to me that if my nickels were dimes and my dimes were quarters, I would have $21.25. How many dimes and nickels are in my box?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +n+ = the number of nickels in the box
Let +d+ = the number of dimes in the box
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(1) +5n+%2B+10d+=+1000+ ( in cents )
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Also given:
(2) +10n+%2B+25d+=+2125+
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(1) +n+%2B+2d+=+200+
(2) +2n+%2B+5d+=+425+
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Multiply both sides of (1) by +2+
and subtract (1) from (2)
(2) +2n+%2B+5d+=+425+
(1) +-2n+-+4d+=+-400+
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+d+=+25+
and
(1) +n+%2B+2d+=+200+
(1) +n+%2B+2%2A25+=+200+
(1) +n+=+200+-+50+
(1) +n+=+150+
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There are 150 nickels and 25 dimes in the box
check:
(1) +5%2A150+%2B+10%2A25+=+1000+
(1) +750+%2B+250+=+1000+
(1) +1000+=+1000+
and
(2) +10%2A150+%2B+25%2A25+=+2125+
(2) +1500+%2B+625+=+2125+
(2) +2125+=+2125+
OK