More Mathematicky Stuff...

Three mathematicky-type things for those who like them...


-1. All Derfs are Enajs. One-third of all Enajs are Derfs. Half of all Sivads are Enajs. One Sivad is a Derf. Eight Sivads are Enajs. The number of Enajs is 90. How many Enajs are neither Derfs nor Sivads?

-2. Two boats leave opposite sides of a still river (no cross-currents) simultaneously and head straight for the opposite bank. meeting at 300 yards north of the south bank. When they each reach the opposite bank they do an about-turn (in their own time) and the second time they meet they are 400 yards south of the north bank. Assuming both boats maintain a constant speed throughout, what is the width of the river?

-3. Mrs Worrier put three little bags on the table. "Hey, pudgy" she said (she was a great loss to the Diplomatic Corps, I've always thought). "Look at the different types of chocolate I bought with the two pounds I found in the pocket of your jeans when I washed them."

"What did they cost?" said I, ever the tight-fist.

"Well", she said,. "I got five ounces of one kind, six of another, and seven of the third. One cost nine pence an ounce less than what I'd have paid for an ounce of each of the other two. There was no change from the money that I found in your jeans. Oh - and one type of chocolate was 10 pence per ounce." (That's her all over - incapable of giving a straight answer to a straight question)

What was the cost of the other two types of chocolate?

This is probably a more logicky approach than mathematicky

1

"All Derfs are Enajs."
"One-third of all Enajs are Derfs."
"The number of Enajs is 90."

So..
Enajs = 90
Derfs = 30
60 Enajs are not Derfs. (1)


"Half of all Sivads are Enajs."
"Eight Sivads are Enajs."
"One Sivad is a Derf."

So..
Sivads = 16
Of the 60 Enajs from (1), 7 are Sivads. (2)

So..
The number of Enajs that are neither Derfs nor Sivads
= 60 Enajs from (1) - 7 Sivads from (2) = 53 Enajs

2. Two boats leave opposite sides of a still river (no cross-currents) simultaneously and head straight for the opposite bank. meeting at 300 yards north of the south bank. When they each reach the opposite bank they do an about-turn (in their own time) and the second time they meet they are 400 yards south of the north bank. Assuming both boats maintain a constant speed throughout, what is the width of the river?

Cinq cents.

A = boat 1st going South, B = other boat, w = width of river

1st meeting: A travelled w - 300, B travelled 300

2nd meeting: A travelled 300 + w-400 = w - 100;
B travelled w-300 + 400 = w + 100

Since speeds constant, distance ratios are constant:
A/B = (w - 300) / 300 = (w - 100) / (w + 100)
w^2 - 300w + 100w - 30000 = 300w - 30000
w^2 - 500w = 0
w^2 = 500w
w = 500

Excellent solves, gentlemen!

I'm sure that "chocolaty experience" took place
when Mrs W visited Canada, and that she spent
$200, and one brand was $10 per ounce!

"One cost nine DOLLARS an ounce less than what
I'd have paid for an ounce of each of the other two."
a + 9 = 10 + b
b = a - 1 ; so one brand was a Loonie less than the other.

If 5 ounces @ $10: $150 left for the 6ers and 7ers:
6a + 7(a - 1) = 150: 13a = 157 : no!
7a + 6(a - 1) = 150 : 13a = 12 : YES!
7 * $12 = $84; 6 * $11 = $66; 84 + 66 = 150

If 6 ounces @ $10: no solution
If 7 ounces @ $10: no solution

Soooo...Ladies and Gents, here you have it:
5 ounces @ $10
6 ounces @ $11
7 ounces @ $12

So in today's pounds that'd be...

6.3065 British pounds sterling
6.9371 British pounds sterling
7.5678 British pounds sterling

Geeezzzz....how can "they" call themselves
civilized and not use the dollars and cents

Nice solve Denis - wish we still had pounds, shillings and pence!

You don't? What you got now?