Question

Manuel pays a flat rate of $105 for his cell phone. He is also charged $0.12 for every text that he sends. His cell phone bill can be no more than the amount he has budgeted for it each month. Which of the following is a possible scenario for the amount Manuel has budgeted for his cell phone?

Manuel sends 40 texts and has budgeted $110 for his cell phone bill. (My answer)



Manuel sends 60 texts and has budgeted $111 for his cell phone bill.



Manuel sends 80 texts and has budgeted $113 for his cell phone bill.



Manuel sends 100 texts and has budgeted $116 for his cell phone bill.

Answer 1

Manuel sends 40 texts and has budgeted $110 for his cell phone bill

Step-by-step explanation:

We are given that:

The flat rate is $105 and the charge is $0.12 per text.

Assuming Manuel sends x texts, the equation used to calculate the amount he'll pay will be:

y = 0.12x + 105

where y is the amount he pays, x is the number of texts he sent and 105 is the flat rate

Now, let's consider each of the given scenarios:

1- First scenario:

If Manuel sends 40 texts, then he'll pay:

y = 0.12(40) + 105 = $109.8

We are given that Manuel budgeted $110 which is almost equivalent to the amount he'll pay, therefore, this scenario is possible

2- Second scenario:

If Manuel sends 60 texts, then he'll pay:

y = 0.12(60) + 105 = $112.2

We are given that Manuel budgeted $111 which is less than the amount he'll pay, therefore, this scenario is not possible

3- Third scenario:

If Manuel sends 80 texts, then he'll pay:

y = 0.12(80) + 105 = $114.6

We are given that Manuel budgeted $113 which is less than the amount he'll pay, therefore, this scenario is not possible

4- Fourth scenario:

If Manuel sends 100 texts, then he'll pay:

y = 0.12(100) + 105 = $117

We are given that Manuel budgeted $116 which is less than the amount he'll pay, therefore, this scenario is not possible

Based on the above:

The first scenario is the correct one

Hope this helps :)