Boy makes the most points in his basketball
career and wants to know how many he made.
His previous record of 18, and he made more
than that. Only made 2 pointers and 3 pointers,
and made 3 times for 2 pointers than 3
pointers. Made no more than 8 two pointers.
How many 3 pointers and how many 2 pointers
did he make?
Let x be the number of 3 pointers made and y be the number of 2 pointers made.
Given:
- Boy's total points scored is greater than 18.
- Boy only made 2 and 3 pointers.
- Boy made 3 times more 2 pointers than 3 pointers.
- Boy made no more than 8 two pointers.
We can create the following equations:
3x + 2y > 18 (Total points scored is greater than 18)
y = 3x (Boy made 3 times more 2 pointers than 3 pointers)
y ≤ 8 (Boy made no more than 8 two pointers)
Substitute y = 3x into the first equation:
3x + 2(3x) > 18
3x + 6x > 18
9x > 18
x > 2
Since x must be an integer value, the minimum value of x is 3 (as x cannot be equal to 2).
From y = 3x:
y = 3(3)
y = 9
Therefore, the boy made 3 three-pointers and 9 two-pointers.