Hi 2e2,
Here's some puzzles for you to solve! Hint.. all can be solved using algebra!
LEVEL 1
What number gives the same results when it is added to 1.5 as when it is multiplied by 1.5?
LEVEL 2
Peter picked one pebble more than Paul. Pat picked one pebble more than Pam. Peter and Paul picked 10 more pebbles than Pam and Pat. Peter, Paul, Pam and Pat picked 60 pebbles in total. How many pebbles did Peter pick?
LEVEL 3
A certain number consists of two digits. The number is equal to five times the sum of its digits. If you add 9 to the number, its order of its digit is reversed. What is the number?
Alright, that's all for today. Once again, well done 2e2, for completing your homework on time! Keep up the good job!
PS: Please post your answers [and workings if any] in the comments session. Keep the blog going!
Miss Gina
Here's some puzzles for you to solve! Hint.. all can be solved using algebra!
LEVEL 1
What number gives the same results when it is added to 1.5 as when it is multiplied by 1.5?
LEVEL 2
Peter picked one pebble more than Paul. Pat picked one pebble more than Pam. Peter and Paul picked 10 more pebbles than Pam and Pat. Peter, Paul, Pam and Pat picked 60 pebbles in total. How many pebbles did Peter pick?
LEVEL 3
A certain number consists of two digits. The number is equal to five times the sum of its digits. If you add 9 to the number, its order of its digit is reversed. What is the number?
Alright, that's all for today. Once again, well done 2e2, for completing your homework on time! Keep up the good job!
PS: Please post your answers [and workings if any] in the comments session. Keep the blog going!
Miss Gina
posted by Miss Gina at
10:28 PM
10 Comments:
1st question;
3+1.5 = 4.5
3*1.5 = 4.5
Ans : 3
1st comment =D
This comment has been removed by the author.
Question 3;
By trial and error method
12+9 = 21
23+9 = 32
34+9 = 43
45+9 = 54
56+9 = 65
.......
There's a pattern there.
45+9 = 54 -- Reversed
(4+5)*5 = 9*5 = 45
Answer : 45
Well Done Frits !!!
Correct answer for both questions.
Now, who can solve the same two questions using algebra?
Hint: Let x be .....
This comment has been removed by the author.
This comment has been removed by the author.
let's x be the number, y be the munber of result.
x+1.5=y ---1
1.5x=y ---2
subts 2 into 1
x+1.5=1.5x
1.5=1.5x-x
1.5=0.5x
3=x
Ans: the number is 3
KoUn=D
question 1 :
let a be the unknown number ,
let b be the unknown result .
a + 1.5 = b ---> 1
a x 1.5 = b ---> 2
1.5a = b ---> 3
from 3 into 1
a + 1.5 = 1.5a
1.5 = 1.5a - a
1.5 = 0.5a
a = 3
unknown number : 3
question 2 :
let a be the number of pebbles Paul collected .
let b be the number of pebbles Pam collected .
Paul ---> a
Peter ---> a + 1
Pam ---> b
Pat ---> b + 1
Peter and Paul ---> b + b + 1 + 10
= 2b + 11
2b + 11 = a + a + 1
2b + 11 = 2a + 1
2b + 11 + b + b + 1 = 4b + 12
4b + 12 = 60 pebbles
4b = 60 - 12
4b = 48
b = 12 pebbles
Pam ---> 12 pebbles
Pat ---> 12 + 1 = 13 pebbles
Peter and Paul ---> 60 - 13 - 12
= 35 pebbles
2b + 11 = 2a + 1 = 35
2a + 1 = 35
2a = 35 - 1
2a = 34
a = 17
Paul ---> 17 pebbles
Peter ---> 17 + 1 = 18 pebbles
Peter picked up 18 pebbles .
question 3 :
let x be digit 1 ,
let y be digit 2 ,
let n be the unknown number .
n = xy ---> 1
n = 5 ( x + y ) ---> 2
n = 5x + 5y ---> 3
n + 9 = yx ---> 4
let x be 1 ,
let y be 2 .
n = 12
n = 5 ( 1 + 2 )
n = 5 + 10
n = 15 - wrong answer .
let x be 2 ,
let y be 3 .
n = 23
n = 5 ( 2 + 3 )
n = 10 + 15
n = 25 - wrong answer .
let x be 3 ,
let y be 4 .
n = 34
n = 5 ( 3 + 4 )
n = 15 + 20
n = 35 - wrong answer .
let x be 4 ,
let y be 5 .
n = 45
n = 5 ( 4 + 5 )
n = 20 + 25
n = 45 - correct answer
45 + 9 = 54
unknown number : 45
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