Question

Velasquez, Miguel, Juan, and Pablo score a total of 36 points in a game of basketball. They score a consecutive even number of points from smallest to greatest in respect to the order of the names mentioned. How many points does Juan score?A6 pointsB12 pointsC8 pointsD10 points

Answer 1

Take into account that the scores are three even consecutive numbers. Being x a missing value we can write:

2x, 2(x+1), 2(x+2), 2(x+3)

where each of the previous expressions corresponds to the score of Velasquez, Migule, Juan and Pablo respectivelly.

Now, due to the sum of all scores are 36 point, we can write:

2x + 2(x+1) + 2(x+2) + 2(x+3) = 36

By applying distribution property left side and by ordering like terms we get:

2x + 2x + 2x + 2x + 2 + 4 + 6 = 36

8x + 12 = 36

Now, by subtracting 12 both sides, simplifying and dividing by 8 we obtain:

8x = 36 - 12

8x = 24

x = 24/8

x = 3

Then, we can replace the previous value into the expression which represents Juan score:

2(x + 2) = 2(3 + 2) = 2(5) = 10

Hence, Juan scored 10 points (option D)