Westonci.ca is your go-to source for answers, with a community ready to provide accurate and timely information. Join our platform to get reliable answers to your questions from a knowledgeable community of experts. Get detailed and accurate answers to your questions from a dedicated community of experts on our Q&A platform.
Sagot :
To solve the given problem, let's start by defining the variables:
- Let [tex]\( p \)[/tex] represent the number of pennies.
- Let [tex]\( n \)[/tex] represent the number of nickels.
According to the problem, we have two pieces of information:
1. The total value of the pennies and nickels is $8.80.
2. There are twice as many nickels as there are pennies.
We can set up the following system of equations based on the given information:
1. The first equation comes from the total value of the pennies and nickels:
[tex]\[ 0.01p + 0.05n = 8.80 \][/tex]
2. The second equation comes from the relationship between the number of nickels and pennies:
[tex]\[ n = 2p \][/tex]
Now, let's solve these equations step-by-step.
### Step 1: Substitute the value of [tex]\( n \)[/tex] from the second equation into the first equation
From the second equation, we know:
[tex]\[ n = 2p \][/tex]
Substitute [tex]\( n \)[/tex] into the first equation:
[tex]\[ 0.01p + 0.05(2p) = 8.80 \][/tex]
### Step 2: Simplify the equation
Distribute the 0.05 through the parentheses:
[tex]\[ 0.01p + 0.10p = 8.80 \][/tex]
Combine like terms:
[tex]\[ 0.11p = 8.80 \][/tex]
### Step 3: Solve for [tex]\( p \)[/tex]
To isolate [tex]\( p \)[/tex], divide both sides of the equation by 0.11:
[tex]\[ p = \frac{8.80}{0.11} \][/tex]
[tex]\[ p = 80 \][/tex]
So, Madi has 80 pennies.
### Step 4: Solve for [tex]\( n \)[/tex]
Use the second equation to find [tex]\( n \)[/tex]:
[tex]\[ n = 2p \][/tex]
[tex]\[ n = 2 \times 80 \][/tex]
[tex]\[ n = 160 \][/tex]
So, Madi has 160 nickels.
### Solution:
Madi has 80 pennies and 160 nickels.
To summarize:
[tex]\[ \begin{array}{c} 0.01p + 0.05n = 8.80 \\ n = 2p \end{array} \][/tex]
The values are:
[tex]\[ p = 80, \quad n = 160 \][/tex]
Thus, Madi has 80 pennies and 160 nickels.
- Let [tex]\( p \)[/tex] represent the number of pennies.
- Let [tex]\( n \)[/tex] represent the number of nickels.
According to the problem, we have two pieces of information:
1. The total value of the pennies and nickels is $8.80.
2. There are twice as many nickels as there are pennies.
We can set up the following system of equations based on the given information:
1. The first equation comes from the total value of the pennies and nickels:
[tex]\[ 0.01p + 0.05n = 8.80 \][/tex]
2. The second equation comes from the relationship between the number of nickels and pennies:
[tex]\[ n = 2p \][/tex]
Now, let's solve these equations step-by-step.
### Step 1: Substitute the value of [tex]\( n \)[/tex] from the second equation into the first equation
From the second equation, we know:
[tex]\[ n = 2p \][/tex]
Substitute [tex]\( n \)[/tex] into the first equation:
[tex]\[ 0.01p + 0.05(2p) = 8.80 \][/tex]
### Step 2: Simplify the equation
Distribute the 0.05 through the parentheses:
[tex]\[ 0.01p + 0.10p = 8.80 \][/tex]
Combine like terms:
[tex]\[ 0.11p = 8.80 \][/tex]
### Step 3: Solve for [tex]\( p \)[/tex]
To isolate [tex]\( p \)[/tex], divide both sides of the equation by 0.11:
[tex]\[ p = \frac{8.80}{0.11} \][/tex]
[tex]\[ p = 80 \][/tex]
So, Madi has 80 pennies.
### Step 4: Solve for [tex]\( n \)[/tex]
Use the second equation to find [tex]\( n \)[/tex]:
[tex]\[ n = 2p \][/tex]
[tex]\[ n = 2 \times 80 \][/tex]
[tex]\[ n = 160 \][/tex]
So, Madi has 160 nickels.
### Solution:
Madi has 80 pennies and 160 nickels.
To summarize:
[tex]\[ \begin{array}{c} 0.01p + 0.05n = 8.80 \\ n = 2p \end{array} \][/tex]
The values are:
[tex]\[ p = 80, \quad n = 160 \][/tex]
Thus, Madi has 80 pennies and 160 nickels.
Answer:
80 pennies
160 nickles
Step-by-step explanation:
8.80 = p(0.01) + n(0.05)
n=2p
substitution
8.80=p(0.01) + 2p(0.05)
*100 to both sides for simplicity.
880=p+2p(5)
880=11p
80=p
80 pennies
160 nickles
We appreciate your time. Please come back anytime for the latest information and answers to your questions. We hope you found what you were looking for. Feel free to revisit us for more answers and updated information. Get the answers you need at Westonci.ca. Stay informed with our latest expert advice.
