ChunkerPanda100

You must alternate children and adults to meet the rule, so that leaves 2 child spots and 3 adult spots you have to randomize. The child spots can be randomizes 2 ways, and the adult spots can be randomized 6 ways. 12 ways total.

The answer is 6/23

Ellen can choose 1*2*3= 6 tiles that are different from steve.

There is a total of 23 different tiles because Steve already took one and 24-1=23. 

so it is 6/23

I think the two equations should be like this....

If Alice receives n dollars from Bob, then she will have 3 times as much money as Bob.

A + n  =  3 * (B - n)

If she gives n dollars to Bob, then she will have 2 times as much money as Bob.

A - n  =  2 * (B + n)

So we have..

A + n  =  3B - 3n    →     A  =  3B  - 4n     →     3A  =  9B   - 12n

A - n  =  2B + 2n    →     A  =  3B + 3n     →     4A  =  12B + 12n        Add these two to get..

7A  =  17B     →     7A / B  =  17     →     A / B  =  17 / 7
 

this one was hard

Consider                                                                ab4  =  48  

We will divide both sides by ab.  

Since ab=72, we will divide the left side  

by "ab" and the right side by its equal 72.  

                                                                              ab4         48  

                                                                             ——   =   ——  

                                                                              ab           72  

Note that ab4 = (ab) * (b3)  

Cancel ab out of the left side.  

Reduce 48/72 on the right side.  

                                                                               b3           2  

                                                                             ——   =   ——  

                                                                                1            3  

                                                                                 b   =   cube root of (2 / 3)  

Seven integers    n  + n+1   n+2 ....... n+6    =   7n + 21

    equals   6 * (n+6) = 6n+36

7n+21  = 6n+36

n = 15    the smallest

thanks to ElectricPavlov

 d−4=5(g−4)................(1)

d==5(g - 4) + 4

d−7=8(g−7)................(2)

5(g - 4) + 4 - 7==8(g - 7)

5g - 20 + 4 - 7==8g - 56

56 - 20 + 4 - 7==8g - 5g

33 == 3g

g==33/3==11 - sub this into (2) above

d - 7==8(11 - 7)

d - 7 ==32

d ==32 + 7 ==39 years - his dad's current age.