Question

Aman, Suresh, and Ekta are playing a video game. Aman has scored $p$ points, Ekta is 6 points behind, and Suresh is 10 points ahead of Aman. The maximum game points that can be scored is 3 points less than 5 times the total score of all three. Express the maximum game points using $p$.

• A. 15$p$ + 17
• B. 12$p$ + 17
• C. 15$p$ + 1
• D. 3$p$ + 1

Answer 1

The correct option is A 15$p$ + 17

Points scored by Aman = $p$

Suresh is 10 points ahead of Aman
So, points scored by Suresh = $p$ + 10

Ekta is 6 points behind Aman,
So, points scored by Ekta = $p$ – 6
Hence, the total points scored by all three of them
= $p$ + ($p$ + 10) + ($p$ - 6)
= 3$p$ + 4

According to the question,
The maximum game points that can be scored is 3 points less than 5 times the total score of all three.

Now,
5 times the total score of all three
= 5(3$p$ + 4)
= 15$p$ + 20 (Using distributive property)
and,
3 less than 5 times the total score of all three
= 15$p$ + 20 – 3
= 15$p$ + 17

Hence, the maximum number of game points is 15$p$ + 17.