Joe has a collection of nickels and dimes that is worth $4.20. If the number of dimes were doubled and the number of nickels were increased by 7, the value of the coins would be $6.65. How many dimes does he have?

d=number of dimes, n=number of nickels

10d+5n=420

10d*2+5(n+7)=665

solution:

second equation: 20d + 5n =665-35=630

from first: 10d = 420 - 5n

substitute in second: 2*(420-5n)+5n=630

840-630=5n

210=5n => n=42

10d=420-5n=420-210=210

=>d=21

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