Young Writers Society

So, I have this maths homework, and I get most of it but I'm totally stuck on a few. If anyone could give me a few hints I would be very grateful.

You have 11 large boxes, each of which is either empty or contains 8 small boxes. Likewise each of these small boxes is either empty or contains 8 even smaller empty boxes. If there are 102 empty boxes in all, how many boxes do you have altogether?

Yeah, I'm completely befuzzled on this one.

In a 2-lap race I complete the first lap at a speed of 10m/s and the second lap at a speed of 20 m/s. What's my average speed for the whole race?

This is probably one of those questions which if totally obvious if you just know the trick, but... I can't figure out the trick.

Edit: I figured this one out by trying different distances. It was indeed extremely obvious.

Show that the product of 3 consecutive numbers is a multiple of six.

I thought for this one you did n + (n+1) + (n+2) = 3n+3 which has to be a multiple of six, but then I realised that that was adding instead of multiplying, and if I try to do it with algebra when multiplying I get n(n+1)(n+2) which gave me n(cubed) + 3n(squared) +3n, which is obviously a multiple of 3, but not always of 6. So, I'm quite confused.

Five football players are preparing for a penalty shoot-out. If the probability of each one scoring is 0.6 what is the probability that three out of the five players score?

I tried to do a tree diagram for this one but it got really squished up and impossible to read, and I can't figure out any other way to do it..

I had a nice long explanatory post, but IE ate it. *grumbles* I don't have time to tackle the first problem right now, but I can help with the last two (sans explanation).

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You expanded wrong. It may be easier to multiply (n^2 * n)(n +2).

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1 player = 60% probability of scoring

Since everyone has an equal probability of scoring, the total probability of the team scoring is 60%.

And so the formula would be 0.6(1/5) + 0.6(1/5) + 0.6(1/5) or 0.6*(3/5).

And here's a tree diagram:


Red = possible scores

Internet explorer Clearly it has malicious intentions. Thankyou so much though!

That makes a lot of sense with the probability one. I think I'd been trying to work it out for if three people scored five times or something..

Why is it (n^2 * n)? Wouldn't it be (n^2 + n) if this comes from n(n+1)? But anyway, I'll try expanding it again.

Thanks again!

It's (n^2 * n) because I typoed and hit * instead of +.

As for the first question, the easiest way to solve it is to work backwards.

Assume that at least one Large box is completely filled, and that all 8 of its Smaller boxes are filled as well. You wind up with 64 empty Smallest boxes.

102 - 64 = 38

Since the Smaller boxes only come in multiples of 8, find the closest multiple of 8 to 38; in this case, it's 32. 32/8 = 4, which is also equal to the number of Large full boxes that contain the 32 empty Smaller boxes.

Tally: 5 Large (full), 32 Smaller (empty), 64 Smallest (empty)

38 - 32 = 6, which is the number of Large empty boxes. As you can see, this matches up to the 11 total Large boxes we're given in the problem (5 + 6 = 11).

And now it's just a matter of tallying up the boxes.

11 + 5(8) + 8(8), or 11 Large + (5 full Large * 8 Smaller) + (8 full Smaller * 8 Smallest).