AvenJohn

2+2x>.6(13+x)

20+20x>78+6x

14x>58

x>58/14

x=5

:D

1+2=3 so the side length of the square on the bottom right is 3.

1+3=4 so the side length of the square on the bottom left is 4.

4+3=7 so the width of the rectangle is 7.

2+2+2-1=5 so the length of the big square is 5.

5+4=9 so the length of the rectangle is 9.

7*9=63 so the area is 63

:D

A) The number of boxes were multiplied by 10 and the time by 2 so the number of machines must be multiplied by 10/2=5 meaning there are 16 additional machines.

B) We have two equations.5B=2M and 8(B+2)=3(M+7). Solving these gets us 12 bears and 32 monkeys so there are 44 total figurines.

C) 7W=10V and 8(W-3)=9(V+3). This gets us Winnie had 30 and Vincy 21. There are 51 total batches.

D) Lets set the uncle's age as U and the grandpa's as G. We are given 3U=G and 4(U-8)=G-8. Therefore U=24 and G=72. Grandpa is 72 years old.

E) Set gold ribbons as G and silver ones as S. We know that 2G=S and 4(G-10)=3(S-32) that gives us G=28 and S=56. Ms. Elizabeth started with 84 ribbons.

F) There are 6 drips every 20 seconds meaning there are 18 a minute. There are 121 minutes (including 10:00 and midnight) and 121*18=2178 so there are 2178 total drips.

:D

We can use the POP formula. 3(3+5)=x(x+6) so 24=x^2+6x meaning x^2+6x-24=0. We can use the quadratic formula to get x=-6+-(sqrt132)/2 which means x=sqrt33-3 because the length can't be negative.

:D

I can't see parts of the solution CPhill.

LOL!

We can bring the y^-2 down to the denominator and divide by the x to get 3x^2/y^5

:D

There are 11 terms and the common ratio is -2. Using the geometric series calculator, the answer is 683.

:D

Thanks Melody. Is there a way to tell if the question is from aops? Often I can't unless there's a lot of rather similar questions together.