Vanessa wants to purchase a new cell phone plan. The two plans from which she can choose are shown below. Vanessa used the syste

Question

3 years ago

14

Vanessa wants to purchase a new cell phone plan. The two plans from which she can choose are shown below. Vanessa used the syste

m of equations shown below to determine how many minutes she can talk on both plans for the monthly costs to be equal. CA = 22 + 0.13m CB = 44 + 0.09(m –100) When using substitution to solve the system of equations, what is a reasonable solution? When Vanessa has used the phone for 775 minutes, the cost for Plan A and the cost for Plan B will both be $122.75. When Vanessa has used the phone for 325 minutes, the cost for Plan A and the cost for Plan B will both be $64.25. When Vanessa has used the phone for 32.5 minutes, the cost for Plan A and the cost for Plan B will both be $26.23. When Vanessa has used the phone for 764 minutes, the cost for Plan A and the cost for Plan B will both be $121.32.

Mathematics

1 answer:

user100 [1] · Answer 1 · 2021-12-24T02:16:17+03:00

Answer:

2. 325 minutes.

Step by step explanation:

We will substitute our given number of minutes in our both equation one by one to find the correct option.

1. Let us substitute m= 775 in both equations.

$CA=22+0.13m$

$CA=22+0.13\cdot 775$

$CA=22+100.75=122.75$

$CB=44+0.09(m-100)$

$CB=44+0.09(775-100)$

$CB=44+0.09\cdot675$

$CB=44+60.75=104.75$

$104.75\neq122.75$

We can see that both plans have different costs , therefore, 1st option is incorrect.

2. Let us substitute m= 325 in both equations.

$CA=22+0.13m$

$CA=22+0.13\cdot 325$

$CA=22+42.25=64.25$

$CB=44+0.09(m-100)$

$CB=44+0.09(325-100)$

$CB=44+0.09\cdot 225$

$CB=44+20.25=64.25$

$64.25=64.25$

When Vanessa has used the phone for 325 minutes, the cost for Plan A and the cost for Plan B will both be $64.25.Therefore, 2nd option is correct choice.

3. Let us substitute m= 32.5 in both equations.

$CA=22+0.13m$

$CA=22+0.13\cdot 32.5$