Question

Help please!

So far this basketball season, all of Nikkis points have come
from two-point and three-point field goals. She has scored a
total of 43 points. The number of three-point field goals she
has made is one more than twice as many two-point field
goals. How many of each type of field goal has Nikki made?

Answer 1

Answers:

• 5 two-pointers
• 11 three-pointers

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Step-by-step explanation:

x = number of two-pointers made

2x+1 = number of three-pointers made

This is because of the fact that she made one more than twice as many three-pointers than two-pointers.

In other words,

number of three pointers = 2*(number of two pointers) + 1

number of three pointers = 2x + 1

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If she made x two-pointers, then she gets 2x points from just those made shots.

If Nikki made 2x+1 three-pointers, then she gets 3(2x+1) = 6x+3 points from just the stuff beyond the arc.

In total, she earns (2x)+(6x+3) = 8x+3 points from both types of shots.

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Set this equal to the stated total 43 points and solve for x.

8x+3 = 43

8x = 43-3

8x = 40

x = 40/8

x = 5

Nikki made 5 two-pointers and 2x+1 = 2*5+1 = 11 three-pointers

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Check:

A = points from two-pointers only = 2*5 = 10 points

B = points from three-pointers only = 3*11 = 33 points

A+B = total points = 10+33 = 43 points

The answer has been confirmed.