Question

Carolyn has $2.55 in her purse in nickels and dimes. The number of nickels in nine less than three times the number of dimes. Find the number of each type of coin

Answer 1

This is a system of equations problem. Let x be the number of dimes and y be the number of nickels.

From the problem, we know the following:

x + y = n (where n is the total number of coins)

y = 3x - 9 (because the number of nickels is three times the number of dimes minus nine)

We also know that the total value of the coins is $2.55 and that a dime is worth $0.10 and a nickel is worth $0.05. So we can create an equation using the total value of the coins:

0.10x + 0.05y = 2.55

Now we have a system of three equations and three variables. To solve for x, y and n, we can use substitution or elimination method.

First equation and second equation:

x+3x-9 = n

4x-9=n

4x = n+9

x = (n+9)/4

By substituting the value of x in equation 3

0.10*(n+9)/4 + 0.05*(3*(n+9)/4-9) = 2.55

Solving this equation we get n = 63

Thus, x = (63+9)/4 = 18 dimes

y = 3x - 9 = 3*18 - 9 = 45 nickels

So, Carolyn has 18 dimes and 45 nickels.