He can either pay a $150 joining fee and a $10 monthly fee or he can pay a $50 joining fee and a $30 monthly fee. on what month will the cumulative costs of the plans be equal and what will those total costs be?

it will take 5 months for the cumulative costs of the plans to be equal and the total cos is $200

Step-by-step explanation:

Let x represent the number of months that for which the cumulative costs of the plans will be equal.

Let y represent the total cost of using plan A for x months.

Let z represent the total cost of using plan B for x months.

He can either pay a $150 joining fee and a $10 monthly fee. This means that the total cost of using plan A would be

y = 150 + 10x

For plan B, he can pay a $50 joining fee and a $30 monthly fee. This means that the total cost of using plan B would be

y = 50 + 30x

To determine the number of hours for which the cumulative costs of the plans will be equal, we would equate y to z. It becomes

150 + 10x = 50 + 30x

30x - 10x = 150 - 50

20x = 100

x = 100/20 = 5 months

The total cost would be

150 + 10 × 5 = 150 + 50 = $200

the answer will be