Word problems algebra

Question

I have $34 coins Some quarters and some are nickels. The quarters are worth $5.20 more than the nickels. How many of each coin do I have?

Answer 1

11 Nickels, 23 Quarters sum to 34

Let Q = number of quarters

N= the number of nickels

do the math with cents, not dollars

Q+N=34

25Q=520+5N = 520 +5(34-Q)

25Q=520+170-5Q

30Q=690

3Q=69

Q=69/3 = 23

N= 34-13= 11

11 Nickels and 23 Quarters

At first though it seemed to read $34 worth of coins, but that can't be right, as follows

25Q+5N=3400 cents

5Q+N=680

N=680-5Q

25Q=520+5N

25Q=520+5(680-5Q) =520+ 3400-25Q

50Q=520+3400=3920

5Q=392

Q=78 2/5

N=680-5Q=680-392=288

288 Nickels, 78.4 Quarters, which doesn't really make sense to have 2/5 or 4/10 of a quarter

Yet if you check, the math is correct

5(288)+25(78.4) = 1440+1960=3400 cents = $34

and the value of the quarters = $19.60 which is $5.20 more than $14.40 the value of the nickels