Question

A. Write an equation that can be used to determine the number of text messages Jacob and Roberto can send for their plan to cost the same

B. Solve the equation form part A to find the number of text messages each person can send for their costs to be the same

Answer 1

y = 0.15t + 20
y = 0.10t + 30

0.15t + 20 = 0.10t + 30 <== ur equation
0.15t - 0.10t = 30 - 20
0.05t = 10
t = 10 / 0.05
t = 200 <== each person can send 200 texts for their plans to cost the same

Answer 2

Jacob's and Roberto's equations are illustrations of linear functions.

• The equations are: $\mathbf{Jacob: y = 20 + 0.15x}$ and $\mathbf{Roberto: y = 30 + 0.10x}$
• The number of text messages each person can send for their costs to be the same is 200

(a) The equations

From the question, we have the following highlights

• Jacob's plan: $20 per month + $0.15 per text
• Roberto's plan: $30 per month + $0.10 per text

Let the monthly charge be y and the number of texts be x.

The equations are:

$\mathbf{Jacob: y = 20 + 0.15x}$

$\mathbf{Roberto: y = 30 + 0.10x}$

(b) The number of texts to spend an equal amount

This means that:

$\mathbf{y = y}$

So, we have:

$\mathbf{20 + 0.15x = 30 + 0.10x}$

Collect like terms

$\mathbf{ 0.15x -0.10x= 30 -20 }$

$\mathbf{ 0.05x= 10 }$

Divide both sides by 0.05

$\mathbf{x= 200 }$

Hence, the number of text messages is 200

Read more about linear equations at:

https://brainly.com/question/11897796