Question

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

Answer 1

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\\eq122.75`

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`

`CA=22+4.225=26.225`

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

`CB=44+0.09(32.5-100)`

`CB=44+0.09\cdot -67.5`

`CB=44-6.075=37.925`

`37.925\\eq26.225`

4. Let us substitute m= 764 in both equations.

`CA=22+0.13m`

`CA=22+0.13\cdot 764`

`CA=22+99.32=121.32`

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

`CB=44+0.09(764-100)`

`CB=44+0.09\cdot 664`

`CB=44+59.76=103.76`

`121.32\\eq103.76`

Therefore, 4th option is incorrect.