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Select the correct answer.

A total of 22 dimes and nickels have a value of [tex]$\$[/tex] 1.90[tex]$. If $[/tex]d[tex]$ represents the number of dimes and $[/tex]n[tex]$ represents the number of nickels, which system of equations models this situation?

A. $[/tex]d + n = 1.9[tex]$
\[
0.1d + 0.05n = 22
\]

B. $[/tex]d + n = 22[tex]$
\[
0.1d + 0.05n = 1.9
\]

C. $[/tex]d + n = 1.9[tex]$
\[
0.1d + 0.5n = 22
\]

D. $[/tex]d + n = 22$
[tex]\[
0.1d + 0.5n = 19
\][/tex]



Answer :

GinnyAnswer
To solve this problem, we need to model the situation using a system of equations.

Denote:
- [tex]\( d \)[/tex] as the number of dimes
- [tex]\( n \)[/tex] as the number of nickels

We are provided with two key pieces of information:
1. A total of 22 coins (dimes + nickels)
2. A total value of [tex]$1.90 from these coins Let's break this down step by step: 1. Total Number of Coins: - We are told that there are 22 coins in total. This can be expressed mathematically as: \[ d + n = 22 \] 2. Total Value of Coins: - Each dime is worth $[/tex]0.10.
- Each nickel is worth [tex]$0.05. - The total value of the 22 coins is $[/tex]1.90.
- Therefore, the sum of the value of the dimes and the value of the nickels should equal $1.90. This can be expressed mathematically as:
[tex]\[ 0.10d + 0.05n = 1.90 \][/tex]

Putting these two equations together, the system of equations that models the given situation is:

[tex]\[ \begin{cases} d + n = 22 \\ 0.10d + 0.05n = 1.90 \end{cases} \][/tex]

Now, let's identify the correct answer from the given options:

A.
[tex]\( \begin{cases} d + n = 1.9 \\ 0.1d + 0.05n = 22 \end{cases} \)[/tex]
- This is incorrect.

B.
[tex]\( \begin{cases} d + n = 22 \\ 0.1d + 0.05n = 1.9 \end{cases} \)[/tex]
- This is correct.

C.
[tex]\( \begin{cases} d + n = 1.9 \\ 0.1d + 0.5n = 22 \end{cases} \)[/tex]
- This is incorrect.

D.
[tex]\( \begin{cases} d + n = 22 \\ 0.1d + 0.5n = 19 \end{cases} \)[/tex]
- This is incorrect.

Therefore, the correct answer is B.

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