Question

Karan needs to choose between two gym plans. He can either pay a \$150$150dollar sign, 150 joining fee and a \$10$10dollar sign, 10 monthly fee, or he can pay a \$50$50dollar sign, 50 joining fee and a \$30$30dollar sign, 30 monthly fee. On what month will the cumulative costs of the plans be equal, and what will those total costs be?

Answer 1

For the first plan:
Joining fee = $150
monthly fee = $10
Cumulative cost in x months = $(150 + 10x)

For second plan:
Joining fee = $50
monthly fee = $30
Cumulative cost in x months = $(50 + 30x)

Let the cumulative costs of both plan are equal after x months.

$50 + 30x = 150 + 10x \\ \\ 30x - 10x = 150 - 50 \\ \\ 20x = 100 \\ \\ x = \frac{100}{20} = 5 \: months$

On 5th month, the cumulative costs will be equal.

Cost = 50 + 5×30 = 50 + 150 = $200