Zi and Tina scored 19 points. Tina and Mom scored 14 points. Tina scored as many points as Zi and Mom did together. How many points did each player score?

Question

This is about basketball 

Answer 1

Let Z = Zi, T = Tina, and M = Mom

Here's what we know:

Z + T = 19 (Zi and Tina together made 19 points)

M + T = 14 (Mom and Tina together made 14 points)

T = M + Z (Tina made as many points as Mom and Zi together)

 

We have a value for T, so let's plug it into the two equations:

Z + M + Z = 19

2Z + M = 19

 

M + M + Z = 14

2M + Z = 14

 

From here, we can use the elimination method to remove one of the variables by multiplying one of the equations by -2, or by isolating one of the variables. I'll be using elimination in this case.

-2(2M + Z = 14) → -4M - 2Z = -28

 

2Z  +  M = 19

-2Z - 4M = -28

----------------------

-3M = -9

Divide both sides by -3:

M = 3

 

Now that we know M, we can solve for Z:

2M + Z = 14

2 * 3 + Z = 14

6 + Z = 14

Z = 8

 

T = M + Z

T = 3 + 8

T = 11

 

Now to check:

T + Z = 19

11 + 8 = 19

19 = 19

 

M + T = 14

3 + 11 = 14

14 = 14