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Math Fun #1168132
11/04/18 01:28 PM
11/04/18 01:28 PM
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Upstate NY
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-1. When I add 2 times my age 2 years from now to 3 times my age 3 years from now, I get 6 times my current age. How old will I be 5 years from now?"

2. Arrange the numbers 1-32 in a circle so that any two adjacent numbers sum to a square number. For Example : 1-8-28 ... ( 1+8=sq(3) and 8+28=sq(6) )

-3. Three circles are bound together by a rubber band as shown in the figure. Assume the diameter of each circle is 10 cm; then how long is the rubber band if it is stretched as shown?



-4. Mick and John were in a 100 meter race. When Mick crossed the finish line, John was only at the 90 meter mark. Mick suggested they run another race. This time, Mick would start ten meters behind the starting line. All other things being equal, will John win, lose, or will it be a tie in the second race?



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Re: Math Fun [Re: Pandora] #1168143
11/04/18 07:33 PM
11/04/18 07:33 PM
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MICK:@m............100..............>t
JOHN:@j...........90..........>t
100/m = 90/j : j = 9m / 10

@m.................110........................>110/m
***10***@j...............100..............>100/j = 100/(9m/10)

110/m - 100/(9m/10)
= 110/m - 1000/(9m)
= 990/(9m) - 1000/(9m)
= -10/(9m) : so poor John loses again !!


I'm a man of few words, BUT I use 'em often!!
Re: Math Fun [Re: Pandora] #1168146
11/04/18 07:54 PM
11/04/18 07:54 PM
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Right you are, Denis! wave


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Re: Math Fun [Re: Pandora] #1168181
11/05/18 05:58 AM
11/05/18 05:58 AM
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Mojave desert, California
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3.


Line segments, AB, CD, and EF are all 10cm in length.
Arc BC spans 120deg of the circle.
Circumference of the circle is 10pi so

Length of arc BC is (120/360)10pi = (10/3)pi

Length of the rubber band = 10+10+10+3(10/3)pi = 30+10pi smile

Re: Math Fun [Re: Pandora] #1168191
11/05/18 09:10 AM
11/05/18 09:10 AM
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Perfectly done! wave


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Re: Math Fun [Re: Pandora] #1168195
11/05/18 09:25 AM
11/05/18 09:25 AM
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1. Let x be your current age.
2(x+2) + 3(x+3) = 6x
5x + 13 = 6x
13 = x
Your current age is 13, 5 years from now your age will be 18 wave


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Re: Math Fun [Re: Pandora] #1168196
11/05/18 09:32 AM
11/05/18 09:32 AM
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1. You will be 18 in 5 years time, being 13 now - (2 x 15) + (3 x 16) = 78 = 6 x 13

Probably feels like only yesterday! grin

Last edited by Lex; 11/05/18 09:33 AM.

Life is what happens while you're making other plans.

Re: Math Fun [Re: Pandora] #1168197
11/05/18 09:36 AM
11/05/18 09:36 AM
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More mathematical integrity in manxman's answer - mine was trial and error. smile


Life is what happens while you're making other plans.

Re: Math Fun [Re: Pandora] #1168219
11/05/18 12:45 PM
11/05/18 12:45 PM
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Both correct! wave


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Re: Math Fun [Re: Pandora] #1168222
11/05/18 12:51 PM
11/05/18 12:51 PM
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Originally Posted By: Pandora
2. Arrange the numbers 1-32 in a circle so that any two adjacent numbers sum to a square number. For Example : 1-8-28 ... (1+8=sq(3) and 8+28=sq(6))

Morning walk analysis:
- arranging in straight line ok, but 1st + last = a square
- 32+31 = 63: so 64 too high, so 49 = highest square
- possible squares are 4,9,16,25,36,49
- using 32: 32+4=36 and 32+17=49 are only possibilities

Hope someone solves soon, cause I'm now kinda stuck!!!


I'm a man of few words, BUT I use 'em often!!
Re: Math Fun [Re: Pandora] #1168224
11/05/18 01:11 PM
11/05/18 01:11 PM
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Posts: 52,940
Upstate NY
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Good analysis. 4 and 17 do appear on each side of 32. grin


Netflix needs to stop asking if I'm still watching and start asking if I've switched the laundry over yet
Re: Math Fun [Re: Pandora] #1168303
11/06/18 03:05 AM
11/06/18 03:05 AM
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Isle of Man
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Enough variables for quite a few morning walks, but I am sure there will be an equation for this... crazy


Life is what happens while you're making other plans.

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