QuestionGaby's piggy bank contains dimes and nickels worth $\$ 4.00$ . If she has 54 coins in all, how many of each does she have?
Gaby has $\square$ dimes and $\square$ nickels in her piggy bank.

Studdy Solution

STEP 1

1. Gaby's piggy bank contains only dimes and nickels.
2. The total value of the coins is $4.00.
3. Gaby has a total of 54 coins.
4. We need to find the number of dimes and nickels.

STEP 2

1. Define variables for the number of dimes and nickels.
2. Write equations based on the given conditions.
3. Solve the system of equations.

STEP 3

Define variables for the number of dimes and nickels.
Let $d$ represent the number of dimes and $n$ represent the number of nickels.

STEP 4

Write equations based on the given conditions.
Equation 1: The total number of coins is 54. $d + n = 54$
Equation 2: The total value of the coins is $4.00. Since dimes are worth$ 0.10 and nickels are worth $0.05, we have: \[ 0.10d + 0.05n = 4.00 \]

STEP 5

Solve the system of equations.
First, solve Equation 1 for one of the variables. Let's solve for $n$ : $n = 54 - d$
Substitute $n = 54 - d$ into Equation 2: $0.10d + 0.05(54 - d) = 4.00$
Simplify and solve for $d$ : $0.10d + 2.70 - 0.05d = 4.00$
Combine like terms: $0.05d + 2.70 = 4.00$
Subtract 2.70 from both sides: $0.05d = 1.30$
Divide by 0.05: $d = \frac{1.30}{0.05}$ $d = 26$
Now, use the value of $d$ to find $n$ : $n = 54 - d$ $n = 54 - 26$ $n = 28$
Gaby has $\boxed{26}$ dimes and $\boxed{28}$ nickels in her piggy bank.

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