Q&A - PSLE Math
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YumYum:
HiHi all, I'd appreciate yr help for the foll Qn:
Separate the following 8 numbers 26, 34, 57, 65, 69, 95, 119, 161 into 2 groups, each with 4 numbers so that the product of the 4 numbers in each group is equal.
thanks!
26 = 2 x 13
34 = 2 x 17
57 = 3 x 19
65 = 5 x 13
69 = 3 x 23
95 = 5 x 19
119 = 7 x 17
161 = 7 x 23
Group 1 --> 26 (2 x 13) , 69 (3 x 23), 95 (5 x19), 119 (7x17)
Group 2 --> 34 (2 x 17) , 57 (3 x 19), 65 (5x 13), 161 (7 x 23)
cheers. -
Hi MathIzzzFun,
Thanks for your help!
Good Nite
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Would somebody please check this (extract from My Pals are Here, Maths Homework - P6)
Question
-----------
The ratio of Jame’s age to Andy’s age is 2:7. In 8 years time, the ratio will become 2:5. Find Jame’s present age.
Answer
---------
Eqn 1: J/A = 2/7 -> 7J=2A
Eqn 2: (J+8) / (A+8) = 2/5 -> 5J + 40 = 2A + 16
Substitute eqn 1 into eqn 2
5J + 40 = 7J +16
7J-5J = 40-16
2J = 24
J = 12
James present age is 12 years old.
James : Andy
2 : 7
12 : 42
Andy is 42 years old.
After 8 years
James : Andy
2 : 5
20 : 50 (or 12+8 : 42+8) -
Is there a simpler method to solve this question (extract from My Pals are Here, Maths Homework, Primary 6A)
Question
-----------
Keith and Shawn each have some money. If Keith spends $38, the ratio of the amount of money Keith has to the amount of money Shawn has will become 2:5. If Shawn spends $38, the ratio will become 8:13. How much money does each boy have?
Answer
--------
Eqn 1: (K-38)/S = 2/5 -> 2S = 5K-190
Eqn 2: K/(S-38) = 8/13 -> 13K = 8S-304
Substitute eqn 1 into eqn 2 to get
13K = 4 (5K-190) - 304
K = 152
Solve eqn 1 using K=152
S = ((5x152) -190)/2 = 285
Keith has $152 and Shawn has $285 -
MathAche:
HiWould somebody please check this (extract from My Pals are Here, Maths Homework - P6)
Question
-----------
The ratio of Jame's age to Andy's age is 2:7. In 8 years time, the ratio will become 2:5. Find Jame's present age.
Answer
---------
Eqn 1: J/A = 2/7 -> 7J=2A
Eqn 2: (J+8) / (A+8) = 2/5 -> 5J + 40 = 2A + 16
Substitute eqn 1 into eqn 2
5J + 40 = 7J +16
7J-5J = 40-16
2J = 24
J = 12
James present age is 12 years old.
James : Andy
2 : 7
12 : 42
Andy is 42 years old.
After 8 years
James : Andy
2 : 5
20 : 50 (or 12+8 : 42+8)
Age difference will remain the same.
Present-
James : Andy --> 2 : 7 --> 6u : 21u
8 years' time-
James : Andy --> 2 : 5 --> 10u : 25u
So, 4u --> 8, 1u--> 2
Present age :
James --> 6u = 12 years old
Andy --> 21u --> 42 years old.
cheers. -
MathAche:
HiIs there a simpler method to solve this question (extract from My Pals are Here, Maths Homework, Primary 6A)
Question
-----------
Keith and Shawn each have some money. If Keith spends $38, the ratio of the amount of money Keith has to the amount of money Shawn has will become 2:5. If Shawn spends $38, the ratio will become 8:13. How much money does each boy have?
Answer
--------
Eqn 1: (K-38)/S = 2/5 -> 2S = 5K-190
Eqn 2: K/(S-38) = 8/13 -> 13K = 8S-304
Substitute eqn 1 into eqn 2 to get
13K = 4 (5K-190) - 304
K = 152
Solve eqn 1 using K=152
S = ((5x152) -190)/2 = 285
Keith has $152 and Shawn has $285
Total amount Keith and Shawn had left in both cases are the same.
Keith spends $ 38:
Keith : Shawn --> 2:5 --> 6u : 15u (total 21u)
Shawn spends $38:
Keith : shawn --> 8u : 13u (total 21u)
so 2u --> $38, 1u--> $19
Keith's money --> 8u --> 8 x $ 19 = $ 152
Shawn's money --> 15u --> 15 x $ 19 = $ 285
cheers. -
MathIzzzFun:
HiMathAche:
Would somebody please check this (extract from My Pals are Here, Maths Homework - P6)
Question
-----------
The ratio of Jame's age to Andy's age is 2:7. In 8 years time, the ratio will become 2:5. Find Jame's present age.
Answer
---------
Eqn 1: J/A = 2/7 -> 7J=2A
Eqn 2: (J+8) / (A+8) = 2/5 -> 5J + 40 = 2A + 16
Substitute eqn 1 into eqn 2
5J + 40 = 7J +16
7J-5J = 40-16
2J = 24
J = 12
James present age is 12 years old.
James : Andy
2 : 7
12 : 42
Andy is 42 years old.
After 8 years
James : Andy
2 : 5
20 : 50 (or 12+8 : 42+8)
Age difference will remain the same.
Present-
James : Andy --> 2 : 7 --> 6u : 21u
8 years' time-
James : Andy --> 2 : 5 --> 10u : 15u
So, 4u --> 8, 1u--> 2
Present age :
James --> 6u = 12 years old
Andy --> 21u --> 42 years old.
cheers.
MathIzzzFun.
typo error in your solution,
It should be 25u instead of 15u
cheers. -
small:
HiMathIzzzFun:
[quote=\"MathAche\"]Would somebody please check this (extract from My Pals are Here, Maths Homework - P6)
Question
-----------
The ratio of Jame's age to Andy's age is 2:7. In 8 years time, the ratio will become 2:5. Find Jame's present age.
Answer
---------
Eqn 1: J/A = 2/7 -> 7J=2A
Eqn 2: (J+8) / (A+8) = 2/5 -> 5J + 40 = 2A + 16
Substitute eqn 1 into eqn 2
5J + 40 = 7J +16
7J-5J = 40-16
2J = 24
J = 12
James present age is 12 years old.
James : Andy
2 : 7
12 : 42
Andy is 42 years old.
After 8 years
James : Andy
2 : 5
20 : 50 (or 12+8 : 42+8)
Age difference will remain the same.
Present-
James : Andy --> 2 : 7 --> 6u : 21u
8 years' time-
James : Andy --> 2 : 5 --> 10u : 25u
So, 4u --> 8, 1u--> 2
Present age :
James --> 6u = 12 years old
Andy --> 21u --> 42 years old.
cheers.
MathIzzzFun.
typo error in your solution,
It should be 25u instead of 15u
cheers.[/quote]thanks .. partially into dream land...
cheers. -
Hi MathIzzzFun,
Separate the following 8 numbers 26, 34, 57, 65, 69, 95, 119, 161 into 2 groups, each with 4 numbers so that the product of the 4 numbers in each group is equal.
26 = 2 x 13
34 = 2 x 17
57 = 3 x 19
65 = 5 x 13
69 = 3 x 23
95 = 5 x 19
119 = 7 x 17
161 = 7 x 23
Group 1 –> 26 (2 x 13) , 69 (3 x 23), 95 (5 x19), 119 (7x17)
Group 2 –> 34 (2 x 17) , 57 (3 x 19), 65 (5x 13), 161 (7 x 23)
You’re a whizz at numbers!!! Can you share how you figured this one out? Honestly, I’d be stumped were I faced with such a question! Given the time constraint in an exam, even with a calculator, it’d have taken me ages. -
anneshirleygilbert:
HiHi MathIzzzFun,
Separate the following 8 numbers 26, 34, 57, 65, 69, 95, 119, 161 into 2 groups, each with 4 numbers so that the product of the 4 numbers in each group is equal.
26 = 2 x 13
34 = 2 x 17
57 = 3 x 19
65 = 5 x 13
69 = 3 x 23
95 = 5 x 19
119 = 7 x 17
161 = 7 x 23
Group 1 --> 26 (2 x 13) , 69 (3 x 23), 95 (5 x19), 119 (7x17)
Group 2 --> 34 (2 x 17) , 57 (3 x 19), 65 (5x 13), 161 (7 x 23)
You're a whizz at numbers!!!! Can you share how you figured this one out? Honestly, I'd be stumped were I faced with such a question! Given the time constraint in an exam, even with a calculator, it'd have taken me ages.
the first 4 numbers gave clues to using factors to solve this problem...
26 - 2 x 13
34 - 2 x 17
57 - 3 x 19
65 - 5 x 13
So, once the factors for the remaining numbers are worked out, what is left is just to group the numbers by factors - either by 2,3,5,7 or 13,15,17,19
cheers.
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