I have finished Summer Work all but this one. Denver beat the Giants in a game. The sum of their scores was 44. The difference of their scores was 20. How many points did Denver score? I don't want the answer, I just want to know how to figure it out. Thank You for any help you can give me.
D + G = 44
D - G = 20
Hi Ms. Sue. I was glad to see you out there. 24 is not the answer is it? That sounds too easy! I guess I do need the answer but I truly want to know how to get to it. Thank You sooooo much Ms. Sue
Nope. Denver did not score 24 points. It doesn't fit the problem.
D = 44 - G
44 - G - G = 20
44 - 2G = 20
24 = 2G
12 = G
So, anything over the difference you divide in half and give each team a half? I tried this with different numbers and it seemed to work. I think I have it now. Thank You again Ms. Sue, for all your help.
You're welcome, Kyle.
To figure out how many points Denver scored in the game, you can use a system of equations to represent the given information. Let's denote Denver's score as "D" and the Giants' score as "G."
From the given information:
1. "Denver beat the Giants in a game" implies that Denver's score (D) is greater than the Giants' score (G), so D > G.
2. "The sum of their scores was 44" can be written as the equation: D + G = 44.
3. "The difference of their scores was 20" can be written as the equation: D - G = 20.
We now have a system of two equations with two variables:
D + G = 44
D - G = 20
To solve this system, we can use the method of substitution or elimination. Let's use the method of elimination.
By adding the two equations together, we eliminate the variable G:
(D + G) + (D - G) = 44 + 20
Simplifying, we get:
2D = 64
Dividing both sides of the equation by 2, we find:
D = 32
Therefore, Denver scored 32 points in the game.
You can check your answer by substituting the values back into the original equations and confirming that they satisfy both equations.