Question

The cost, c, of a health club membership is related linearly to its length in months, m. If a 12-month membership costs $260 and an 18-month membership costs $380, which equation can be used to find the cost of a 30-month membership?

Answer 1

Question :- The cost, c, of a health club membership is related linearly to its length in months, m. If a 12-month membership costs $260 and an 18-month membership costs $380, which equation can be used to find the cost of a 30-month membership?

A) c - 380 = 1/20(30-18)

B) c - 18 = 20(380-30)

C) c - 380 = 20(30-18)

D) c - 18 = 20(30-12)

Solution :-

Let us assume that, x is the fixed price of membership and after that, we have to give , y each month.

So, we can say that,

→ c = x + ym . { c = cost , m = length in months.}

Now, we have given that, a 12- month membership costs $260.

So,

→ x + 12y = 260 ---------- Eqn.(1)

Also, an 18-month membership costs $380.

So,

→ x + 18y = 380 ------------ Eqn.(2)

subtracting Eqn.(1) from Eqn.(2) , we get,

→ (x + 18y) - (x + 12y) = 380 - 260

→ x - x + 18y - 12y = 120

→ 6y = 120

→ y = 20 .

putting value of y in Eqn.(1),

→ x + 12*20 = 260

→ x = 260 - 240

→ x = 20 .

Therefore,

→ The cost of a 30-month membership :-

→ c = x + ym

→ c = 20 + 30*20

→ c = 20 + 600

→ c = $620 .

Now, when put value of c in options and check which one is correct .

Checking Option (C) :-

→ c - 380 = 20(30-18)

→ 620 - 380 = 20 * 12

→ 240 = 240 (Satisfy.)

Hence, Option (C) is Correct Answer.

See also :-

There are some cows, hens and goats in Baburam's fam His 8 year-old son, Vistinu, is fond of counting One day, he counts...

https://brainly.in/question/24178769