Thank you for visiting You have a total of 21 coins all nickels and dimes The total value is tex 1 70 tex Which of the following is the. This page is designed to guide you through key points and clear explanations related to the topic at hand. We aim to make your learning experience smooth, insightful, and informative. Dive in and discover the answers you're looking for!
Answer :
Answer:
Choice D.
Step-by-step explanation:
Let's start by what we know. A nickel is 5 cents (0.05), and a dime
is 10 cents (0.10).
We can represent n and d as variables for each, knowing that the total
amount of coins is 21. So, let's create our first equation: n + d = 21!
Next, the question tells us that the total amount of money spent is 1.70.
Knowing this, we can use the respective values of a nickel and dime to create our second equation: 0.05 + 0.10d = 1.70.
Putting these two equations together, our answer corresponds to D.
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Rewritten by : Jeany
Let's break down the problem into parts and find which system of linear equations accurately represents the scenario involving nickels and dimes.
1. Identify the Variables and Equations:
- We are given a total number of coins:
[tex]\[ n + d = 21 \][/tex]
where [tex]\( n \)[/tex] is the number of nickels and [tex]\( d \)[/tex] is the number of dimes.
- We are also given the total value of the coins:
[tex]\[ 0.05n + 0.10d = 1.70 \][/tex]
The value of a nickel is \[tex]$0.05 and the value of a dime is \$[/tex]0.10.
2. Check Each Option:
Let's analyze each system of linear equations to see which one matches our statements above:
- Option 1:
[tex]\[ n + d = 21 \][/tex]
[tex]\[ 5n + 10d = 1.70 \][/tex]
This equation cannot be correct because the coefficient for the value of the dimes and nickels isn't in dollars. It should be represented in cents.
- Option 2:
[tex]\[ n + d = 21 \][/tex]
[tex]\[ 0.10n + 0.05d = 1.70 \][/tex]
This option switches the coefficients for the nickels and dimes incorrectly. Per our scenario, the value of a nickel is \[tex]$0.05 and the value of a dime is \$[/tex]0.10.
- Option 3:
[tex]\[ n + d = 1.70 \][/tex]
[tex]\[ 0.05n + 10d = 21 \][/tex]
This option is clearly incorrect because the total number of coins cannot be \$1.70, and the coefficients do not match our value system.
- Option 4:
[tex]\[
\begin{array}{l}
n + d = 21 \\
0.05n + 0.10d = 1.70
\end{array}
\][/tex]
This option correctly represents the number of coins and their total value based on the value of nickels and dimes. The first equation ([tex]\(n + d = 21\)[/tex]) indicates the total number of coins, and the second equation ([tex]\(0.05n + 0.10d = 1.70\)[/tex]) correctly represents the total monetary value.
The correct system of linear equations that represent this scenario is:
[tex]\[
\begin{array}{l}
n + d = 21 \\
0.05n + 0.10d = 1.70
\end{array}
\][/tex]
Therefore, the answer is option 4.
1. Identify the Variables and Equations:
- We are given a total number of coins:
[tex]\[ n + d = 21 \][/tex]
where [tex]\( n \)[/tex] is the number of nickels and [tex]\( d \)[/tex] is the number of dimes.
- We are also given the total value of the coins:
[tex]\[ 0.05n + 0.10d = 1.70 \][/tex]
The value of a nickel is \[tex]$0.05 and the value of a dime is \$[/tex]0.10.
2. Check Each Option:
Let's analyze each system of linear equations to see which one matches our statements above:
- Option 1:
[tex]\[ n + d = 21 \][/tex]
[tex]\[ 5n + 10d = 1.70 \][/tex]
This equation cannot be correct because the coefficient for the value of the dimes and nickels isn't in dollars. It should be represented in cents.
- Option 2:
[tex]\[ n + d = 21 \][/tex]
[tex]\[ 0.10n + 0.05d = 1.70 \][/tex]
This option switches the coefficients for the nickels and dimes incorrectly. Per our scenario, the value of a nickel is \[tex]$0.05 and the value of a dime is \$[/tex]0.10.
- Option 3:
[tex]\[ n + d = 1.70 \][/tex]
[tex]\[ 0.05n + 10d = 21 \][/tex]
This option is clearly incorrect because the total number of coins cannot be \$1.70, and the coefficients do not match our value system.
- Option 4:
[tex]\[
\begin{array}{l}
n + d = 21 \\
0.05n + 0.10d = 1.70
\end{array}
\][/tex]
This option correctly represents the number of coins and their total value based on the value of nickels and dimes. The first equation ([tex]\(n + d = 21\)[/tex]) indicates the total number of coins, and the second equation ([tex]\(0.05n + 0.10d = 1.70\)[/tex]) correctly represents the total monetary value.
The correct system of linear equations that represent this scenario is:
[tex]\[
\begin{array}{l}
n + d = 21 \\
0.05n + 0.10d = 1.70
\end{array}
\][/tex]
Therefore, the answer is option 4.
