
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
Grade: 7 Age: 12 School:
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.

Anthony from Canada
Grade: 8 9 Age: 14 School:
Solution:
Q1: 735
Q2: 90
If one # is x, then the other is 825x
Then because of P(x)=DQ+R, x=(825x)(8)+15
x=66008x+15
9x=6615 x=735 <====== answer one
825x=90 <=== answer two
About me: I love math and currently skip two grades in regular
skool.. n i like science and computers too...

Tasia Twomey from australia
Grade: 5 Age: 10 School:
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.

Akansh Murthy from USA
Grade: 7 Age: 12 School:
Solution:
Q1: 735,90
x+y=825..(1)
Let x be the bigger # and y be the smaller one. therefore.. x=8y+15..(2)
x8y=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=82590 x=735
Therefore the bigger # is 735 and the smaller number is 90.
About me: i luv basketball and football and i like to read.

Cynthia from Paramount ca
Grade: Age: 22 School:
Solution:
Q1: 735, 90
x= big # y= small #
x+y= 825
8y+15= x
825 y= 8y+ 15
+ y +y

825 0= 9y +15

810 = 9y
810/9 = 9y/9
90 = y
x+ 90= 825
 90= 90

x+ 0= 735
x= 735
y= 90
About me: I love math just haven't practiced it in years. hope
my answer is correct

Joy from USA
Grade: 6 Age: 12 School:
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
About me:

Brady from North America
Grade: 4 Age: 9 School:
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.

Aranshi from USA
Grade: 4 Age: 9 School:
Solution:
Q1:
suppose the numbers are x & y.
So x+y = 825  1
suppose x is bigger number & y is the smaller number so
x8y = 15  2
Solving 1 & 2 you will get
x=735 & y= 90 So the bigger number is 735 & smaller number is
90

Gunsu from USA
Grade: Age: School:
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)

Parth Shah from U.S.A
Grade: 8 Age: 13 School:
Solution:
Q1: bigger no735,smaller no90
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=82515
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.

BJ from USA
Grade: 7 Age: 12 School:

Ivan from canada
Grade: 8 Age: 13 School:

Justin from U.S
Grade: 5 Age: 10 School:

AARTHY from INDIA
Grade: 6 Age: 12 School:

Jaclyn from USA
Grade: 6 Age: 11 School:

Justin from US
Grade: 5 Age: 10 School:

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