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During a football season one team scored 23 goals more than the other. Between them they scored 135 goals.
How many goals did each team score
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There are several ways to solve this and similar problems.
One way to solve for very beginning students
one team scores + team scores = 135 scores, in all.
x + (x - 23) = 135
2x = 135 + 23 = 158
x = 158/2 = 79
ANSWER. One tewm scored 79; the other team scored 79-23 = 56.
CHECK. 79 + 56 = 135 scores, total. ! Correct !
ANOTHER way to solve for more mature students
You write the system of two equations
x + y = 135 (1) (x = one tem scores; y = the other team scores)
x - y = 23 (2)
and add equations.
You get then 2x = 135+23 = 158; x = 158/2 = 79.
As the last step, from equation (1) y = 135 - 79 = 56.
You get the same answer.
Third way for mature experts, who solved such problems tens and hundreds of times
They know that one team get half the sum of given numbers 
= 79,
while the other team get half the difference of given numbers 
= 56.
Solved, explained and completed.
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If you want to see a million similar solved problems, look into the lesson
- Word problems that lead to a simple system of two equations in two unknowns
in this site.
Also, you have this free of charge online textbook in ALGEBRA-I in this site
- ALGEBRA-I - YOUR ONLINE TEXTBOOK.
The referred lesson is the part of this online textbook under the topic "Systems of two linear equations in two unknowns".
Save the link to this online textbook together with its description
Free of charge online textbook in ALGEBRA-I
https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson
to your archive and use it when it is needed.
