Problema Solution
John has a collection of quarters, dimes, nickels and pennies worth $1.28. He has two more dimes than quarters. The number of nickels is two more than the number of dimes. If he has twenty coins, how many nickels does he have?
Answer provided by our tutors
Let the number of quarters = x
No of dimes = 2 more than no of quarters = x + 2
No of nickels = 2 more than dimes = x + 2 + 2 = x + 4
He has total 20 coins
So no. of pennies = 20 - (x + x + 2 + x + 4) = 20 - 3x - 6 = 14 - 3x
Now total value of all coins = $1.28
Penny = 0.01$
Nickel = 0.05$
Dime = $0.10
Quarter = $0.25
So
0.01(14-3x) + 0.05(x+4) + 0.1(x+2) + 0.25x = 1.28
0.14 - 0.03x + 0.05x + 0.2 + 0.1x + 0.2 + 0.25x = 1.28
0.37x + 0.54=1.28
0.37x = 0.74
x = 2
So no of nickels = x + 4 = 2 + 4 = 6 nickels ANS