SOLUTION: alex has the same number of nickels and dimes. his mother gives an additional $4 in nickels and dimes. now alex has twice the nickels and three times the dimes he had before. how m

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Question 1026591: alex has the same number of nickels and dimes. his mother gives an additional $4 in nickels and dimes. now alex has twice the nickels and three times the dimes he had before. how much money did he have in the beginning?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +n%5B1%5D+ = number of nickels he started with
Let +d%5B1%5D+ = number of dimes he started with
Let +n%5B2%5D+ = number of nickels his mother gave him
Let +d%5B2%5D+ = number of dimes his mother gave him
--------------------------------------------
(1) +n%5B1%5D+=+d%5B1%5D+
(2) +5n%5B2%5D+%2B+10d%5B2%5D+=+400+ ( in cents )
(3) +n%5B1%5D+%2B+n%5B2%5D+=+2%2An%5B1%5D+
(4) +d%5B1%5D+%2B+d%5B2%5D+=+3%2Ad%5B1%5D+
--------------------------
There are 4 equations and 4 unknowns, so it's solvable
(3) +n%5B1%5D+=+n%5B2%5D+
(4) +2d%5B1%5D+=+d%5B2%5D+
and
(2) +5n%5B2%5D+%2B+10d%5B2%5D+=+400+
(2) +5n%5B1%5D+%2B+2%2A10d%5B1%5D+=+400+
and, from (1)
(2) +5d%5B1%5D+%2B+2%2A10d%5B1%5D+=+400+
(2) +25d%5B1%5D+=+400+
(2) +d%5B1%5D+=+16+
and, from (1),
(2) +n%5B1%5D+=+16+
------------------
+5%2An%5B1%5D+%2B+10%2Ad%5B1%5D+=+5%2A16+%2B+10%2A16+
+5%2An%5B1%5D+%2B+10%2Ad%5B1%5D+=+80+%2B+160+
+5%2An%5B1%5D+%2B+10%2Ad%5B1%5D+=+240+
He had 240 cents, or $2.40 to start with
-----------------
check:
(3) +n%5B1%5D+=+n%5B2%5D+
(3) +n%5B2%5D+=+16+
and
(4) +2d%5B1%5D+=+d%5B2%5D+
(4) +2%2A16+=+d%5B2%5D+
(4) +d%5B2%5D+=+32+
and
+5%2An%5B2%5D+%2B+10%2Ad%5B2%5D+=+5%2A16+%2B10%2A32+
+5%2An%5B2%5D+%2B+10%2Ad%5B2%5D+=+80+%2B+320+
+5%2An%5B2%5D+%2B+10%2Ad%5B2%5D+=+400+
This is correct -his mother gave him $4.00
OK