Answer :
Sure, let's solve this problem step-by-step.
First, let's define our variables:
- [tex]\( p \)[/tex]: the number of pennies.
- [tex]\( d \)[/tex]: the number of dimes.
We are given two pieces of information:
1. The total value of the pennies and dimes is [tex]$\$[/tex]1.50$.
2. There are five times as many pennies as dimes.
We can set up the following equations based on this information:
1. The total value equation:
[tex]\[ 0.01p + 0.10d = 1.50 \][/tex]
2. The relationship between the number of pennies and dimes:
[tex]\[ p = 5d \][/tex]
Now let's solve these equations step-by-step.
### Step 1: Substitute [tex]\( p = 5d \)[/tex] into the total value equation
Given:
[tex]\[ p = 5d \][/tex]
Substitute [tex]\( p \)[/tex] in the first equation:
[tex]\[ 0.01(5d) + 0.10d = 1.50 \][/tex]
### Step 2: Simplify the equation
Now, carry out the multiplication:
[tex]\[ 0.05d + 0.10d = 1.50 \][/tex]
Combine like terms:
[tex]\[ 0.15d = 1.50 \][/tex]
### Step 3: Solve for [tex]\( d \)[/tex]
Divide both sides of the equation by [tex]\( 0.15 \)[/tex]:
[tex]\[ d = \frac{1.50}{0.15} \][/tex]
[tex]\[ d = 10 \][/tex]
So, we have found that there are [tex]\( 10 \)[/tex] dimes.
### Step 4: Find the number of pennies
Since [tex]\( p = 5d \)[/tex]:
[tex]\[ p = 5 \times 10 \][/tex]
[tex]\[ p = 50 \][/tex]
So, there are [tex]\( 50 \)[/tex] pennies.
### Conclusion
Amber has:
- [tex]\( 50 \)[/tex] pennies
- [tex]\( 10 \)[/tex] dimes
First, let's define our variables:
- [tex]\( p \)[/tex]: the number of pennies.
- [tex]\( d \)[/tex]: the number of dimes.
We are given two pieces of information:
1. The total value of the pennies and dimes is [tex]$\$[/tex]1.50$.
2. There are five times as many pennies as dimes.
We can set up the following equations based on this information:
1. The total value equation:
[tex]\[ 0.01p + 0.10d = 1.50 \][/tex]
2. The relationship between the number of pennies and dimes:
[tex]\[ p = 5d \][/tex]
Now let's solve these equations step-by-step.
### Step 1: Substitute [tex]\( p = 5d \)[/tex] into the total value equation
Given:
[tex]\[ p = 5d \][/tex]
Substitute [tex]\( p \)[/tex] in the first equation:
[tex]\[ 0.01(5d) + 0.10d = 1.50 \][/tex]
### Step 2: Simplify the equation
Now, carry out the multiplication:
[tex]\[ 0.05d + 0.10d = 1.50 \][/tex]
Combine like terms:
[tex]\[ 0.15d = 1.50 \][/tex]
### Step 3: Solve for [tex]\( d \)[/tex]
Divide both sides of the equation by [tex]\( 0.15 \)[/tex]:
[tex]\[ d = \frac{1.50}{0.15} \][/tex]
[tex]\[ d = 10 \][/tex]
So, we have found that there are [tex]\( 10 \)[/tex] dimes.
### Step 4: Find the number of pennies
Since [tex]\( p = 5d \)[/tex]:
[tex]\[ p = 5 \times 10 \][/tex]
[tex]\[ p = 50 \][/tex]
So, there are [tex]\( 50 \)[/tex] pennies.
### Conclusion
Amber has:
- [tex]\( 50 \)[/tex] pennies
- [tex]\( 10 \)[/tex] dimes