When a surfer \"hangs ten, \" he or she has feet placed on a surfboard so that a

Question

When a surfer "hangs ten, " he or she has feet placed on a surfboard so that all ten toes hang over the edge. "Hang five" is the term used for when just one foot is positioned so that all the toes hang over. On this particularly fine surfing day, Rosco Rat is practicing in the big waves with several other surfers. (They are all humans with ten toes each, just like Rosco.) One-fourth of the other surfers are hanging five. Three-eighths of the other surfers are hanging NO toes over any surfboard edges. The rest of the other surfers, not counting Rosco, are hanging ten. There are a total of 120 toes hanging in this competition. How many surfers are practicing today, including Rosco? How many surfers are hanging ten? Is Rosco hanging ten, hanging five or hanging zero?

Explanation / Answer

1.

Let there by n other surfers hanging

So,n/4 are hanging five

3n/8 are hanging no toes

Other ie n-n/4-3n/8=3n/4-3n/8=3n/8 are hanging 10

So total number of toes hanging by other surfers(excluding Rosco) are:

5n/4+10*3n/8=20n/4=5n

Let Rosco be hanging k toes so

5n+k=120

n+k/5=24

n=24-k/5

Now note that:k can be 0 ,1 or 2

But n must be a multiple of 8 because 3/8 of n are hanging no toes.

SO k=0

n=24

So total number of surfers hanging are:n+1=25

2. Number of surfers hanging ten are:3n/8=3*24/8=9

3.

Rosco is hanging zero

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