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Answer :
To determine how many text messages were sent, we equate the costs of the two plans.
Jada's plan is given by:
[tex]$$
c = 0.05t + 5,
$$[/tex]
and Zeke's plan is given by:
[tex]$$
c = 0.10t.
$$[/tex]
Since the costs are the same, we set the two equations equal to each other:
[tex]$$
0.05t + 5 = 0.10t.
$$[/tex]
Next, subtract [tex]$0.05t$[/tex] from both sides to get the terms involving [tex]$t$[/tex] on one side:
[tex]$$
5 = 0.10t - 0.05t.
$$[/tex]
Simplify the right-hand side:
[tex]$$
5 = 0.05t.
$$[/tex]
Now, solve for [tex]$t$[/tex] by dividing both sides by [tex]$0.05$[/tex]:
[tex]$$
t = \frac{5}{0.05}.
$$[/tex]
Calculating the division gives:
[tex]$$
t = 100.
$$[/tex]
Thus, Jada and Zeke each sent [tex]$100$[/tex] text messages in that month.
Jada's plan is given by:
[tex]$$
c = 0.05t + 5,
$$[/tex]
and Zeke's plan is given by:
[tex]$$
c = 0.10t.
$$[/tex]
Since the costs are the same, we set the two equations equal to each other:
[tex]$$
0.05t + 5 = 0.10t.
$$[/tex]
Next, subtract [tex]$0.05t$[/tex] from both sides to get the terms involving [tex]$t$[/tex] on one side:
[tex]$$
5 = 0.10t - 0.05t.
$$[/tex]
Simplify the right-hand side:
[tex]$$
5 = 0.05t.
$$[/tex]
Now, solve for [tex]$t$[/tex] by dividing both sides by [tex]$0.05$[/tex]:
[tex]$$
t = \frac{5}{0.05}.
$$[/tex]
Calculating the division gives:
[tex]$$
t = 100.
$$[/tex]
Thus, Jada and Zeke each sent [tex]$100$[/tex] text messages in that month.
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