this is the hardest problem people said it was the hardest andf they can not solve it
can anyone solve this please it is hard
In a basketball game, Garrett and Logan scored a total of 19 points. Logan and Ray scored a total of 14 points. Logan scored as many points as Garrett and Ray together. How many points did each player score?
Logan______ Garrett______ Ray_____
To solve this problem, we need to set up a system of equations based on the given information.
Let's assign variables to represent the number of points scored by each player:
- Let L represent the number of points Logan scored.
- Let G represent the number of points Garrett scored.
- Let R represent the number of points Ray scored.
Based on the given information, we can come up with three equations:
1) Garrett and Logan scored a total of 19 points:
G + L = 19
2) Logan and Ray scored a total of 14 points:
L + R = 14
3) Logan scored as many points as Garrett and Ray together:
L = G + R
We now have a system of three equations. To solve it, we can use any method such as substitution or elimination.
Let's use substitution to solve this system. We can start by rearranging equation 3 to solve for G:
G = L - R
Now, substitute this expression for G in equation 1:
L - R + L = 19
2L - R = 19 ---- (equation 4)
Next, substitute the value of L from equation 3 into equation 2:
L + R = 14 ---- (equation 5)
We now have two equations, equation 4 and equation 5, both involving L and R. We can solve this system to find the values of L and R.
Adding equation 4 and equation 5, we get:
2L - R + L + R = 19 + 14
3L = 33
L = 11
Substituting this value back into equation 5:
11 + R = 14
R = 14 - 11
R = 3
Finally, substituting the values of L = 11 and R = 3 into equation 3:
11 = G + 3
G = 11 - 3
G = 8
Therefore, the number of points scored by each player is:
Logan: 11 points
Garrett: 8 points
Ray: 3 points