Question

In order to play in chess tournaments at the Marshall Club, Malik pays a fee to become a member. In addition, he pays a set rate for each tournament in which he competes. After competing in 4 tournaments Malik has paid a total of $85, and after competing in 7 tournaments he has paid a total of $130. Malik's friend Masai gets a discount on membership to the Marshall Club and pays $10 less for the membership fee than Malik. Which linear equation gives the total price, p, Masai will pay to compete in t tournaments at the Marshall Club?

Answer 1

To find the total price p Masai will pay to compete in t tournaments, we first determined the cost per tournament (R) and Malik's membership fee (M) from the given information. Knowing that Masai gets a $10 discount on the membership fee, we formulated the linear equation p = 15 + 15t to represent Masai's total expenses at the Marshall Club.

Step-by-step explanation:

The question involves creating an equation based on linear relationships between membership fees, tournament fees, and the total amount spent by Malik at the Marshall Club. Malik’s expenses for 4 and 7 tournaments are given, which allows us to figure out the cost of membership and the cost per tournament. We're also told that Masai gets a discount on the membership fee that is $10 less than what Malik paid.

First, let's denote the membership fee Malik pays as M and the rate per tournament as R. According to the information given:

4R + M = $85 (after 4 tournaments)

7R + M = $130 (after 7 tournaments)

By subtracting the first equation from the second, we get:
3R = $45, which simplifies to R = $15 per tournament.
Substituting R back into either equation, we find that M = $85 - 4(15) = $25 for Malik’s membership fee.

Now, Masai pays $10 less than Malik for the membership fee, so Masai's membership fee is M - $10 = $25 - $10 = $15. The total price p that Masai will pay to compete in t tournaments at the Marshall Club can be expressed by the equation p = 15 + 15t.