The Mystery Numbers

Problem #105

Deadline to submit the solution: August 31st, 2003

 The sum of two numbers is 825. When you divide the bigger number by the smaller you get 8 and the remainder is 15. Q1.Find these two numbers. Explain.

Solutions

Lisa Fernandez from England
Solution:
Q1: The numbers are 735 and 90

I got the answer by trying out loads of different numbers until i got the right one. The mystery numbers are 735 and 90 because they add up to 825, and if you divide 735 by 90 you get 8 with a remainder 15, which is what you were meant to get.
About me: I like playing the piano and the guitar. My favourite subjects are art drama and maths. I would like to be an astronaut and go to Mars My favourite singer is Avril Lavigne.
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Grade: 8 9 Age: 14 School:
Solution:
Q1: 735
Q2: 90

If one # is x, then the other is 825-x
Then because of P(x)=DQ+R, x=(825-x)(8)+15
x=6600-8x+15
About me: I love math and currently skip two grades in regular skool.. n i like science and computers too...
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Tasia Twomey from australia
Solution:
Q1: 735 and 90

The plan I used was guess and check. So at first I said 725+100 which =825 so then i divided and got the answer 7 rem 25. Then i tried 735+90 and got the answer 825 then i divided it and got the answer 8 rem 15.and it was right
About me: my name is tasia i'm very popular i'm good at sport and my favourite sobject is math and i'm the best person in my classn in times tables and we have got year 6's in our class.
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Akansh Murthy from USA
Solution:
Q1: 735,90

x+y=825..(1)
Let x be the bigger # and y be the smaller one. therefore.. x=8y+15..(2)
x-8y=15..(3) To get the values of x&y subtract equation 3 from 1.
x+1y= 825
-x+8y=-15
___________
0+9y= 810
9y= 810 y= 8109
y= 90
Substitute the value of y=90 in equation 1 to get the value of x.
x+90=825 x=825-90 x=735
Therefore the bigger # is 735 and the smaller number is 90.
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Cynthia from Paramount ca
Solution:
Q1: 735, 90

x= big # y= small #
x+y= 825
8y+15= x
825- y= 8y+ 15
+ y +y
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825- 0= 9y +15
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810 = 9y
810/9 = 9y/9
90 = y
x+ 90= 825
- 90= -90
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x+ 0= 735
x= 735
y= 90
About me: I love math just haven't practiced it in years. hope my answer is correct
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Joy from USA
Solution:
Q1: x=735 y=90

x+y=825
x/y=8 r15 which means x=8y+15 replace the x in x+y by 8y+15 which becomes
8y+15+y=825
solve for y then solve for x
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Solution:
Q1: 735 & 90

I started with 815 divided by 10 and I got 81 with a remainder of 5. I kept going and every time I did a problem I said to myself "The dividend is between thi number and this number". Finally I reached the dividend of 90. I divided and I got 8 with a remainder of 15.
About me: I go to Heights Elementary.
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Aranshi from USA
Solution:
Q1:

suppose the numbers are x & y.
So x+y = 825 --- 1
suppose x is bigger number & y is the smaller number so
x-8y = 15 --- 2
Solving 1 & 2 you will get
x=735 & y= 90 So the bigger number is 735 & smaller number is 90

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Gunsu from USA
Solution:
Q1: A=90 and B=735.

1. Let A, B be two numbers. So, A+B=825
2. Let B be the Big number.
3. So B/A = 8+15/A(8 is quotient, 15 is remainder, when you write improper fraction)
4. So B/A = (8A+15)/A
5. Multiply both sides by A
6. You get B = 8A + 15. Now we know that B = 8A + 15.
7. From step 6, substitue B in step 1
8. A+B = 825 which is A + (8A + 15) = 825 which is 9A + 15 = 825 which is 9A = 825 - 15 = 810.
9. If 9A = 810 then A = 810/9 = 90.
10 If A = 90, B = 735 (as A + B = 825)

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Parth Shah from U.S.A
Solution:
Q1: bigger no-735,smaller no-90

Let the numbers be x and y. Let the bigger number be x and the smaller number be y x+y=825 x/y=8 and the remainderis 15 therefore,
x=8y+15
x+y=825
8y+15+y=825
9y+15=825
9y=825-15
9y=810
y=810/9
y=90
x=8y+15 x=8*90+15
x=720+15
x=735 x is the bigger number and y is the smaller number the bigger number is 735 and the smaller number is 90
About me: my age is 13 and i like to solve difficult math problems and puzzles and tricks.
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BJ from USA
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Justin from U.S
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AARTHY from INDIA
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Jaclyn from USA
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Justin from US
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