Louis T. answered • 11/14/14
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To figure out how to solve this question, try thinking of one with (very) small numbers. This always helps me come up with a method to solve a larger problem.
Let's say the total points scored were 4, and the third graders beat the fourth graders by 2 points. Since there are only a few score combinations that add up to 4 (0+4, 1+3, 2+2), it's pretty easy to see that the score was 3-1 (with the third graders taking the win).
Time to turn that thought process into math. Okay, the total score was 4. If x is the third graders' score and y is the fourth graders' score, the equation for total score is:
x + y = 4
We also know that the third graders won by two points. This means, using the same meanings of x and y:
x - y = 2
We can then use algebra to figure out the team's scores. Using the second equation:
x - y = 2
+ y + y Add y to both sides, to solve for x
x = 2 + y
Then, we can plug in 2 + y anywhere we see an x. Let's plug it into the other equation so that we only are left with one variable:
x + y = 4
(y + 2) + y = 4 Plug in x = y + 2
2y + 2 = 4 Simplify y + y to 2y
- 2 - 2 Subtract 2 from both sides
2y = 2
÷2 ÷2 Divide by 2 on both sides
y = 1
Remember, y is the score of the fourth graders. Now that we know the fourth graders' score, remember that we also know the total score, and we can just subtract the fourth graders' score from the third graders' score to find the total:
4 - y = x
4 - 1 = x Substitute y = 1
3 = x Simplify
The third graders scored 3! That was a very simple example, but hopefully it shows you how to solve your more difficult problem.
