Question

A bag contains a certain number of nickels, dimes , quarters and dollars in the ratio 7:1:8:4 . The total value of the currency of the nickels,dimes,quarters and dollars in the bag is equal to 6450 cents. Calculate number of dimes in the bag (100 cents = 20 nickels = 10 dimes = 4 quarters = 1 dollar)

Answer 1

As 20 nickels = 100 cents, 1 nickel = 5 cents.
As 10 dimes = 100 cents, 1 dime = 10 cents.
As 4 quarters = 100 cents, 1 quarter = 25 cents.
1 dollar = 100 cents.

Let:
# of nickels = 7x
# of dimes = x
# of quarters = 8x
# of dollars = 4x

7x {#of nickels} multiplied by 5 {cent value of 1 nickel} = 35x.
x {# of dimes} multiplied by 10 {cent value of 1 dime} = 10x.
8x {# of quarters} multiplied by 25 {cent value of 1 quarter} = 200x.
4x {# of dollars} multiplied by 100 {cent value of 1 dollar} = 400x.

35x + 10x + 200x + 400x = 6450 cents.
x = 10

Thus, there are 10 dimes in the bag.
Hope it helps!