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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
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