Question

Sherri saves nickels and dimes in a coin purse for her daughter. The total value of the coins in the purse is $0.95. The

number of nickels is 2 less than 5 times the number of dimes. How many nickels and how many dimes are in the coin
purse?

Answer 1

Using a system of equations, we find that Sherri has 3 dimes and 13 nickels in the coin purse, given the information that the total value is $0.95 and the number of nickels is 2 less than 5 times the number of dimes.

Step-by-step explanation:

To solve the problem, let's use algebra. We need to translate the given information into a system of equations. Let's define d as the number of dimes and n as the number of nickels.

We're told the number of nickels is 2 less than 5 times the number of dimes. This gives us the first equation:

n = 5d - 2

Next, we know the total value of the coins is $0.95. Since a nickel is worth $0.05 and a dime is worth $0.10, we have the second equation:

0.05n + 0.10d = 0.95

To solve the system, we can substitute n from the first equation into the second:

0.05(5d - 2) + 0.10d = 0.95

After simplifying, we get:

0.25d - 0.10 + 0.10d = 0.95

0.35d = 1.05

d = 3

Now plug d back into the first equation to find n:

n = 5(3) - 2

n = 13

So, Sherri has 3 dimes and 13 nickels in the coin purse.

Answer 2

Let's represent the number of dimes in the coin purse as d. Then, the number of nickels in the coin purse can be represented as 5d - 2.

The total value of the coins can be expressed as:

0.05 * (5d - 2) + 0.10 * d = 0.95

Expanding and simplifying the equation, we get:

0.05 * 5d - 0.05 * 2 + 0.10 * d = 0.95

0.50d - 0.10 = 0.95

0.50d = 1.05

d = 2.10

Since the number of dimes must be a whole number, we round d down to 2. So, there are 2 dimes in the coin purse and 5 * 2 - 2 = 6 nickels in the coin purse.