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lara31 [8.8K]
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]3 years ago
3 0

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

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\neq26.225

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\neq103.76

Therefore, 4th option is incorrect.




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