SOLUTION: The cross-country teams of East and West run against each other twice each fall. At the first meet, East's score was two thirds of West's score. At the second meet East's score inc
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Question 200326: The cross-country teams of East and West run against each other twice each fall. At the first meet, East's score was two thirds of West's score. At the second meet East's score increased by seven points and West's score decreased by seven points. In the second meet West's score was three less than East's score. How many points did Each team score in each meet?
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The cross-country teams of East and West run against each other twice each fall.
At the first meet, East's score was two thirds of West's score.
At the second meet East's score increased by seven points and West's score
decreased by seven points.
In the second meet West's score was three less than East's score.
How many points did Each team score in each meet?
:
Let x = West's score at the 1st meet
then
x = East's score at the 1st meet
:
" At the second meet East's score increased by seven points and West's score
decreased by seven points."
x + 7 = East's score at the 2nd meet
(x-7) = West's score at the 2nd meet
;
" In the second meet West's score was three less than East's score."
(x - 7) = (x + 7) - 3
x - 7 = x + 4
Multiply b 3 to get rid of the denominator, results
3x - 3(7) = 2x + 3(4)
:
3x - 21 = 2x + 12
:
3x - 2x = 12 + 21
:
x = 33 is West's score at the 1st meet
and
*33 = 22 is East's score at the 1st meet
:
33 - 7 = 26 is West's score at the 2nd meet
and
22 + 7 = 29 is East's score at the 2nd meet
:
Which is a difference of 3
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