Question

bethany has $3.10 in nickels and dimes. she has a total of 44 coins. what is the value of the nickels bethany has? $0.90 $2.60 $1.80 $1.30

Explanation:

Step1: Define variables

Let \( n \) be the number of nickels and \( d \) be the number of dimes. We know two things: the total number of coins is 44, so \( n + d = 44 \), and the total value of the coins is $3.10 (or 310 cents). Since a nickel is 5 cents and a dime is 10 cents, we have the equation \( 5n + 10d = 310 \).

Step2: Simplify the value equation

Divide the equation \( 5n + 10d = 310 \) by 5 to simplify it. We get \( n + 2d = 62 \).

Step3: Solve the system of equations

We have the system:
\[

$$\begin{cases} n + d = 44 \\ n + 2d = 62 \end{cases}$$

\]
Subtract the first equation from the second equation: \( (n + 2d) - (n + d) = 62 - 44 \). This simplifies to \( d = 18 \).

Step4: Find the number of nickels

Substitute \( d = 18 \) into \( n + d = 44 \). So \( n + 18 = 44 \), which means \( n = 44 - 18 = 26 \).

Step5: Calculate the value of nickels

Since each nickel is 5 cents, the value of 26 nickels is \( 26 \times 5 = 130 \) cents, which is $1.30.

Answer:

\$1.30