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#1124679 - 09/12/17 03:09 PM Math Fun
Pandora Offline

Sonic Boomer

Registered: 08/06/00
Posts: 48510
Loc: Upstate NY
-1. ABCD is a square with the length of 20 inches on each side. 4 quarter circumferences are tangented at the center of the square. How many square inches are in the total shaded area?




-2. A five digit number is represented by ABCDE. If we add the number 1 in front of ABCDE, then multiply by 3, the result number will be ABCDE appended by the number 1 (as shown below). What is this five digit number?

1ABCDE x 3 = ABCDE1

-3. In the equation shown, A, B, C, D, and E are 5 consecutive positive integers. What are they?

A^2 + B^2 + C^2 = D^2 + E^2

-4. John, Joe and Jack are having lunch together. John bought 3 pieces of corn bread. Joe bought 2 pieces and Jack bought nothing. John, Joe and Jack decided to share all the bread and had equal amounts of bread for lunch. After lunch, Jack paid 10 dollars to John and Joe. How much money should John and Joe get?
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We do not see things as they are, we see things as we are. - Anais Nin

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#1124680 - 09/12/17 03:31 PM Re: Math Fun [Re: Pandora]
manxman Offline
True Blue Boomer

Registered: 07/23/02
Posts: 20439
Loc: Unionville
3. 10, 11, 12, 13, 14 smile
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Sometimes lost is where you need to be. Just because you don't know your direction doesn't mean you don't have one.

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#1124681 - 09/12/17 03:35 PM Re: Math Fun [Re: Pandora]
CanukDenis Offline
Graduate Boomer

Registered: 11/26/00
Posts: 17751
Loc: Ottawa Ontario Canada
3: b = a+1, c = a+2, d=a+3, e=a+4

a^2 + (a+1)^2 + (a+2)^2 = (a+3)^2 + (a+4)^2
a^2 + a^2+2a+1 + a^2+4a+4 = a^2+6a+9 + a^2+8a+14
Simplifies to:
a^2 - 8a - 20 = 0
Factoring:
(a - 10)(a + 2) = 0
a = 10 or a = -2 ; since positive, a = 10

So 10,11,12,13,14
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#1124690 - 09/12/17 05:14 PM Re: Math Fun [Re: Pandora]
Pandora Offline

Sonic Boomer

Registered: 08/06/00
Posts: 48510
Loc: Upstate NY
Both correct! Dennis gets extra credit for showing his work. lol
_________________________
We do not see things as they are, we see things as we are. - Anais Nin

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#1124713 - 09/12/17 10:56 PM Re: Math Fun [Re: Pandora]
CanukDenis Offline
Graduate Boomer

Registered: 11/26/00
Posts: 17751
Loc: Ottawa Ontario Canada
Originally Posted By: Pandora
4. John, Joe and Jack are having lunch together. John bought 3 pieces of corn bread. Joe bought 2 pieces and Jack bought nothing. John, Joe and Jack decided to share all the bread and had equal amounts of bread for lunch. After lunch, Jack paid 10 dollars to John and Joe. How much money should John and Joe get?

Since Jack's cost is $10, then total cost = $30.
(assumes all 3 guys paid same amount)

Since total cost = $30 and 5 pieces purchased,then
each piece = $6: so John paid $18, Joe paid $12.

So John got $8: 18 - 8 = 10
and Joe got $2: 12 - 2 = 10

Thassa cute li'l problem, Sue...
_________________________
A true friend is a friend in spite of, not because of.

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#1124717 - 09/12/17 11:41 PM Re: Math Fun [Re: Pandora]
Pandora Offline

Sonic Boomer

Registered: 08/06/00
Posts: 48510
Loc: Upstate NY
Well done, Denis. Very clear. smile
_________________________
We do not see things as they are, we see things as we are. - Anais Nin

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#1124719 - 09/13/17 12:29 AM Re: Math Fun [Re: Pandora]
CCbomber Offline
BAAG Specialist

Registered: 01/16/03
Posts: 5421
Loc: Mojave desert, California
1.

Area of a quarter circle = (pi/4)[sqrt(10^2 + 10^2)]^2
= (pi)(50) = 157.08 square inches

Total Area of the shaded region = 4(Area of a quarter circle) - (Area of the square)
= 4(157.08) - 20^2
= 628.32 - 400 = 228.32 square inches

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#1124749 - 09/13/17 08:34 AM Re: Math Fun [Re: Pandora]
Pandora Offline

Sonic Boomer

Registered: 08/06/00
Posts: 48510
Loc: Upstate NY
Spot on, CCb! wave
_________________________
We do not see things as they are, we see things as we are. - Anais Nin

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#1124758 - 09/13/17 10:57 AM Re: Math Fun [Re: Pandora]
CanukDenis Offline
Graduate Boomer

Registered: 11/26/00
Posts: 17751
Loc: Ottawa Ontario Canada
Originally Posted By: Pandora

2. A five digit number is represented by ABCDE. If we add the number 1 in front of ABCDE, then multiply by 3, the result number will be ABCDE appended by the number 1 (as shown below). What is this five digit number?
1ABCDE x 3 = ABCDE1

I must have missed a "simple/quick" way;
I did it this rather "loooooong" way:
I substituted e = 7 since only 7 is possible
to produce a "1" after multiplied by 3:7*3=21.
Initial equation:
3(100000 + 10000a + 1000b + 100c + 10d + 7) =
100000a + 10000b + 1000c + 100d + 70 + 1

Doing the Jailhouse Rock and Peppermint Twist on that monster led to:
70000a + 7000b + 700c + 70d = 299950
Dividing by 70:
1000a + 100b + 10c + d = 4285
Since e = 7 : 42857
With 1 at start and multiplying by 3:
142857 * 3 = 428571

PHEWWWW!!

_________________________
A true friend is a friend in spite of, not because of.

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#1124769 - 09/13/17 12:01 PM Re: Math Fun [Re: Pandora]
CCbomber Offline
BAAG Specialist

Registered: 01/16/03
Posts: 5421
Loc: Mojave desert, California
Here's an easier way, Denis...

1ABCDE x 3 = ABCDE1

(ABCDE+100000)3 = 10(ABCDE)+1
7(ABCDE) = 299999
ABCDE = 42857

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#1124777 - 09/13/17 12:27 PM Re: Math Fun [Re: Pandora]
Pandora Offline

Sonic Boomer

Registered: 08/06/00
Posts: 48510
Loc: Upstate NY
Denis did the Jailhouse Rock and the Peppermint Twist while CCb waltzed through it. Well done, guys! wave
_________________________
We do not see things as they are, we see things as we are. - Anais Nin

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#1124790 - 09/13/17 01:44 PM Re: Math Fun [Re: Pandora]
CanukDenis Offline
Graduate Boomer

Registered: 11/26/00
Posts: 17751
Loc: Ottawa Ontario Canada
Bewteefull CCb!
_________________________
A true friend is a friend in spite of, not because of.

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#1124938 - 09/14/17 07:39 PM Re: Math Fun [Re: CCbomber]
manxman Offline
True Blue Boomer

Registered: 07/23/02
Posts: 20439
Loc: Unionville
Very elegant CCbomber praise
_________________________
Sometimes lost is where you need to be. Just because you don't know your direction doesn't mean you don't have one.

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