A man has 14 coins in his pocket, all of which are dimes and quarters. If the total value of his change is $2.15, how many dimes and how many quarters does he have?

>et d = number of dimes and q = number of quarters

then d + q =14 (the number of coins) [ and q = 14 -d]

and 0.1 d + 0.25 q = 2.15 (the value of the coins)

So 0.1 d + 0.25 (14 -d) = 2.15

10d + 25 ( 14 -d) = 215 by multiplying by 100

10d + 350 - 25d = 215

15d = 135

d = 9

So q = 14 -9 =5

(check 5 *$.25 + 9 * $.10 = 1.25 + 0.90 = $2.15

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