Expert: Scott A Wilson - 9/14/2009

Question
The lenght of a rectangle is 7inches grater than its width.  the perimeter of the rectangle is 50inches.  find the length and width of the rectangle.

luke has test grades of 85,87, and 77 on his first 3 tests. if he wants an average of at least 84 after his 4th test, what are the possible scores he can make on his 4th test?

Answer
Rectangle
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Call L the length and W the width.

We know that L=W+7.  The perimeter is the sum of all the sides, which includes 2 sides of length L and two of length W.  This makes the perimeter P = 2L + 2W.  P is known to be 50.

It is also known that L = W+7, so 2L = 2W+14.  Putting this into P = 2L + 2W for 2L gives
P = 2W + 14 + 2W = 4W + 14.

It is also known that P=50, so 50 = 4W + 14. Subtracting off 14 from both sides gives
36 = 4W.  Dividing both sides by 4 gives W = 9.

Since L is W+7, L is 16.


Test
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Scores: 85, 87, and 77.  Sum of these three is 85+87+77=249.

If the average is to be at least 84, the sum needs to be 4*84=336.

So 336 - 249 is the minimum score he needs to get, which is 87.