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Answer :
To determine the number of text messages Jada and Zeke sent, we need to set their cost equations equal to each other because they paid the same amount in one month.
Here are the cost equations for Jada's and Zeke's plans:
- Jada's Plan: [tex]\( c = 0.05t + 5 \)[/tex]
- Zeke's Plan: [tex]\( c = 0.10t \)[/tex]
Since Jada and Zeke paid the same amount in one month, we set the two cost equations equal to each other:
[tex]\[ 0.05t + 5 = 0.10t \][/tex]
Next, we need to solve for [tex]\( t \)[/tex]:
1. Subtract [tex]\( 0.05t \)[/tex] from both sides to start isolating [tex]\( t \)[/tex]:
[tex]\[ 5 = 0.10t - 0.05t \][/tex]
2. Simplify the equation:
[tex]\[ 5 = 0.05t \][/tex]
3. To solve for [tex]\( t \)[/tex], divide both sides by [tex]\( 0.05 \)[/tex]:
[tex]\[ t = \frac{5}{0.05} \][/tex]
4. Calculate the value:
[tex]\[ t = 100 \][/tex]
Therefore, Jada and Zeke both sent 100 text messages in that month.
In summary, the number of text messages they sent is:
```
100
```
Here are the cost equations for Jada's and Zeke's plans:
- Jada's Plan: [tex]\( c = 0.05t + 5 \)[/tex]
- Zeke's Plan: [tex]\( c = 0.10t \)[/tex]
Since Jada and Zeke paid the same amount in one month, we set the two cost equations equal to each other:
[tex]\[ 0.05t + 5 = 0.10t \][/tex]
Next, we need to solve for [tex]\( t \)[/tex]:
1. Subtract [tex]\( 0.05t \)[/tex] from both sides to start isolating [tex]\( t \)[/tex]:
[tex]\[ 5 = 0.10t - 0.05t \][/tex]
2. Simplify the equation:
[tex]\[ 5 = 0.05t \][/tex]
3. To solve for [tex]\( t \)[/tex], divide both sides by [tex]\( 0.05 \)[/tex]:
[tex]\[ t = \frac{5}{0.05} \][/tex]
4. Calculate the value:
[tex]\[ t = 100 \][/tex]
Therefore, Jada and Zeke both sent 100 text messages in that month.
In summary, the number of text messages they sent is:
```
100
```
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