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