2011-2012 Mathcounts workout 7

#201: To get the surface area you do 2 x ( width x length + length x height + width x height) = 666 so width x length + length x height + width x height = 333
Volume = width x length x height = 720 , 720 = 24 x 5 x 3²
From the surface area you know that two of the dimensions have to be odd numbers to have 
even + even + odd = odd.
Try (5, 3, 48), (15,3, 16) or (5, 9, 16) and you'll see (15, 3, 16) works. The longest length is 16.

#202: (14 x 81 - 10 x 75) divided by 4 = 96

#203:The answer is 0.73.

#204: To find the midpoint, add the two end points and divided the result by 2.
The answer is (4, -6).

#205: T is odd and S is prime and E > T. Write down the prime numbers. There
are 2, 3, 5 and 7. ATE + AT = ROYS You can see that R = 1 and A is 9 and O is
because two numbers adding together the most carry over is 1.T can't be 7 because
that leave only 8 for E and it doesn't work. 5 and 2 encounter similar problems.
So only 934 + 93 = 1027 works.
A + T + E + O = 9 + 3 + 4 + 0 = 16

#206: 2 students = 2/5% so total students are 2 divided by 2.5% =
2 divided by 0.025 = 80 students.

#207: AP : PB = 1: 2 so P is 1/3 x (5-0) = 5/3 away from 5 or 10/3
for the x value and 1/3 times 2 + 0 = 2/3 for the y value.
Plug (10/3, 2/3) to y = kx and you get k = 1/5

#208: Half circumference of the larger circle plus the whole circumference
of the smaller circle = 1/2 of 2r∏ + r∏ = 2∏r.

#209: Let Arlene started with x dollars. The equation would look like this if you keep finding the remaining fraction. {{[(3/5 of x - 4) times 1/2] - 5} times 2/5}- 6 = 2. Working backward and you get x = 90 dollars.

#210:  The first time Judith, Mark and Kelly all received a gift is on the 49th day.
The least common denominator of 6, 5 and 4 is 60.  ( 365 - 49 ) divided by 60 = 5. 26...
5 days plus the first one (the 49th day) is 6 days.