College algebra

Question

A basketball player scored 21 times during one game. She scored a total of 27 ?points, two for each? two-point shot and one for each free throw. How many? two-point shots did sheshe ?make? How many free? throws?

Answer 1

Use a system of equations to represent this problem. Let x be the number of two point shots made and y the number of free throws. You know that the player scored 21 times in the game, which means that x+y=21. You also know that she scored a total of 27 points, which means that 2x+y=27 (each two point shot is worth two points, hence the 2x). Subtract one equation from the other and solve from there to get your answer.

Answer 2

Hello Holly,

 

If I am reading the question correctly the total number of scored shots was 21 and the total number of points was 27. we are also told that she only makes 2 point shots or 1 point shots.  lets call the number of 2 point shots x and the number of 1 point shots y. Now we can write two equations,

 

(eq. 1) x + y = 21 (total number of shots made)

(eq. 2) 2x + y = 27 (we take 2*x because each x shot is worth 2 points)

 

we can then solve this system of equations by elimination or substitution (or graphing),

 

elimination method:

take (eq. 2) and subtract (eq. 1) from it,

 

2x - x + y -y = 27 - 21

 

x = 6 (simplified 2x - x, y - y, 27 - 21)

 

then plug this value for x back into (eq. 1)

 

6 + y = 21

 

y = 21 - 6 (subtracted 6 from both sides)

 

y = 15 (simplified 21 - 6)

 

so she made 6 two point shots, and 15 free throws.

 

Substitution:

 

Solve for y in (eq. 1)

 

y = 21 - x

 

Then plug this into (eq. 2)

 

2x + (21 - x) = 27 

 

now solve for x

 

x + 21 = 27 (simplified 2x - x)

 

x = 27 - 21 (subtracted 21 from both sides)

 

x = 6 (simplified 27 - 21)

 

now plug this into (eq. 1)

 

6 + y = 21

 

y = 21 - 6 (subtracted 6 from both sides)

 

y = 15 (simplified 21 - 6)

 

same answer as before.

 

I hope that this helps. Remember that, in general, if you are solving a system of equations (meaning you have two or more equations with two or more variables) you can use either the elimination or substitution methods. Also, remember that when you don't know the value of something you can always represent that value with a variable like x or y. If you have any questions about these steps please let me know.  Also, if you are ever looking for a regular tutoring session I would be happy to help.