SOLUTION: Mark has 42 coins consisting of dimes and quarters. the total value of his coins is $6. How many of each type of coin does he have? show all your work and explain what method you u

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Question 683734: Mark has 42 coins consisting of dimes and quarters. the total value of his coins is $6. How many of each type of coin does he have? show all your work and explain what method you used to solve the problem.
In advance I will like to say Thank you.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +d+ = number of dimes he has
Let +q+ = number of quarters he has
given:
(1) +d+%2B+q+=+42+
(2) +10d+%2B+25q+=+600+ ( in cents )
----------------------
Multiply both sides of (1) by +10+
and subtract (1) from (2)
(2) +10d+%2B+25q+=+600+
(1) +-10d+-+10q+=+-420+
+15q+=+180+
+q+=+12+
and, since
(1) +d+%2B+q+=+42+
(1) +d+%2B+12+=+42+
(1) +d+=+30+
he has 30 dimes and 12 quarters
check:
(2) +10d+%2B+25q+=+600+
(2) +10%2A30+%2B+25%2A12+=+600+
(2) +300+%2B+300+=+600+
(2) +600+=+600+
OK