Logic Q's: "Beatrice ate 2/3 as many cakes as Annabel would have eaten...."

excinder

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Hey guys, I’m new here. I didn’t know where else to post this, so here goes!!

Beatrice ate 2/3 as many cakes as Annabel would have eaten if Annabel had eaten 6 more than half as many as Beatrice would have eaten if Beatrice had eaten 3 less than Annabel would have eaten. How many cakes did Beatrice eat?

And

“You used to perform on stage, didn’t you Grandad?” asked Peter. “A long time ago” said Grandad. “Tell him what you did” said Peter’s mother. “I was one thousand, two hundred, nothing and one transposed” said Grandad. What act did he perform on stage?

These are most likely trick questions, and I’m usually pretty good at solving them but these ones are pretty tough.
 
We don't customarily give out answers, but this one is a bit ridiculous, and few online seem to have been able to solve it. So:

1. Beatrice ate 2/3 as many cakes as Annabel would have eaten if Annabel had eaten 6 more than half as many as Beatrice would have eaten if Beatrice had eaten 3 less than Annabel would have eaten. How many cakes did Beatrice eat?
Things seem eventually to be defined in terms of what Annabel "would have eaten", so let's pick a variable for that; say, "a".

1. "if Beatrice had eaten 3 less than Annabel would have eaten": a - 3

2. "half as many as (above)": (1/2)(a - 3)

3. "if Annabel had eaten 6 more than (above)": (1/2)(a - 3) + 6

4. "Beatrice ate 2/3 as many as Annabel would have eaten": This means that Annabel would have eaten 3/2 as many as Beatrice ate: a = (3/2)[(1/2)(a - 3) + 6]

. . . . .(1/2)(a - 3) + 6 = (2/3)a

Multiply through by 6 to clear the fractions:

. . . . .a = (3/2)[(1/2)(a - 3) + 6]

. . . . .a = (3/4)(a - 3) + 9/2

. . . . .4a = 3(a - 3) + 18

. . . . .4a = 3a - 9 + 18

. . . . .4a - 3a = 18 - 9

. . . . .a = 9

Look back to see how "a" was defined. Then use this (and the first portion of the exercise) to figure out how many Beatrice ate.

Note: You can check your answer here; it's the answer listed for "Class Challenge No. 10" here. For information on how to do the "translation" (as shown above) of English into math, try here.

“You used to perform on stage, didn’t you Grandad?” asked Peter. “A long time ago” said Grandad. “Tell him what you did” said Peter’s mother. “I was one thousand, two hundred, nothing and one transposed” said Grandad. What act did he perform on stage?
Roman numerals:

* one thousand: M
* two hundred: CC
* and nothing: O
* one transposed (which is still 1): I

Rearrange (as given here) to get "COMIC".

This was not a "math" question! :shock:
 
We don't customarily give out answers, but this one is a bit ridiculous, and few online seem to have been able to solve it. So:


Things seem eventually to be defined in terms of what Annabel "would have eaten", so let's pick a variable for that; say, "a".

1. "if Beatrice had eaten 3 less than Annabel would have eaten": a - 3

2. "half as many as (above)": (1/2)(a - 3)

3. "if Annabel had eaten 6 more than (above)": (1/2)(a - 3) + 6

4. "Beatrice ate 2/3 as many as Annabel would have eaten": This means that Annabel would have eaten 3/2 as many as Beatrice ate: a = (3/2)[(1/2)(a - 3) + 6]

. . . . .(1/2)(a - 3) + 6 = (2/3)a

Multiply through by 6 to clear the fractions:

. . . . .a = (3/2)[(1/2)(a - 3) + 6]

. . . . .a = (3/4)(a - 3) + 9/2

. . . . .4a = 3(a - 3) + 18

. . . . .4a = 3a - 9 + 18

. . . . .4a - 3a = 18 - 9

. . . . .a = 9

Look back to see how "a" was defined. Then use this (and the first portion of the exercise) to figure out how many Beatrice ate.

Note: You can check your answer here; it's the answer listed for "Class Challenge No. 10" here. For information on how to do the "translation" (as shown above) of English into math, try here.


Roman numerals:

* one thousand: M
* two hundred: CC
* and nothing: O
* one transposed (which is still 1): I

Rearrange (as given here) to get "COMIC".

This was not a "math" question! :shock:

DAAAAAAAAAAAAANG!!:-x:-x:-x:-x:-x:-x:-x:-x:eek::eek::eek::eek::eek::eek::eek::eek:
 
* one thousand: M
* two hundred: CC
* and nothing: O
* one transposed (which is still 1): I

Rearrange (as given here) to get "COMIC".

This was not a "math" question! :shock:
That's probably correct but: "O" was not a "Roman numeral for nothing". The Romans did not have a symbol for zero.
 
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