He has d dimes. He has 2 more nickles than dimes, so he has d + 2 nickles. He has 3 times as many pennies as nickles. He has 3(d + 2) pennies.
Now we figure out the value of each type of coin in cents. d dimes are worth 10d cents. d + 2 nickels are worth 5(d + 2) cents. 3(d + 2) pennies are worth 3(d + 2) cents.
Add all expressions of value and set equal to 52 cents.
10d + 5(d + 2) + 3(d + 2) = 52
10d + 5d + 10 + 3d + 6 = 52
18d + 16 = 52
18d = 36
d = 2
He has 2 dimes. He has 2 more nickles than dimes, so he has 2 + 2 nickles, or 4 nickles. <span>He has three times as many pennies as nickels, or 3(4) = 12 pennies.