Question

ben had three times as many nickels as dimes. if the total value of his coins was $1, how many of each kind of coin did he have?

Answer 1

Ben has 4 dimes and 12 nickels

Solution:

Let "d" be the number of dimes

Let "n" be the number of nickels

We know that,

value of 1 dime = $ 0.10

value of 1 nickel = $ 0.05

Ben had three times as many nickels as dimes

Number of nickels = 3 times the number of dimes

n = 3d --------- eqn 1

The total value of his coins was $1

Therefore, we frame a equation as:

number of dimes x value of 1 dime + number of nickels x value of 1 nickel = 1

$d \times 0.10 + n \times 0.05 = 1\\\\\text{Substitute eqn 1 in above }\\\\0.10d + 0.05(3d) = 1\\\\\text{Simplify the above expression }\\\\0.10d + 0.15d = 1\\\\0.25d = 1\\\\\text{Divide both sides of equation by 0.25 }\\\\d = 4$

Substitute d = 4 in eqn 1

n = 3(4)

n = 12

Thus Ben has 4 dimes and 12 nickels