Question

A little lost, would appreciate the help!

In basketball, a successful free throw is worth 1 point, a basket made from inside the 3-point arc is worth 2 points, and a basket made from outside the 3-point arc is worth 3 points. How many of each type of basket did Pilar make?

Answer 1

12 free throws

10 2-pointers

4 3-pointersAnswer:

Explanation:

Answer 2

12 free throws

10 2-pointers

4 3-pointers

Explanation:

Let x = 1 point

y = 2 point

z = 3 point

x + y + z = 26

x = y + 2

x = 3z

Let's make it to where the last two equations are in terms of x

Subtract 2 from both sides of the middle equation

x = y + 2

- 2 - 2

y = x - 2

Divide both sides by 3 in the bottom equation

x/3 = 3z/3

z = x/3

Now plug in the new y and z

x + x - 2 + x/3 = 26

2x + x/3 - 2 = 26

Add 2 to both sides

2x + x/3 - 2 = 26

+ 2 + 2

2x + x/3 = 28

Add up the x terms and don't forget about common denominators

6x/3 + x/3 = 28

7/3x = 28

Multiply both sides by 3/7 to isolate the x variable

(7/3x = 28)3/7

x = 12

Now plug the new x into the original equations to find the remaining variables.

12 = y + 2

- 2 - 2

y = 10

12 = 3z

12/3 = 3z/3

z = 4