i am back , again, and while revising, i came across a couple of questions and i need some clarification:
question 1
If 4 men can make 80 chairs in 12 days, how long will 24 men take to make 300 chairs?
My steps:
4 men --- 80 chairs -- 12 days
1 man -- 20 chairs -- 3 days (take 80 divide by 4 to get 20)
24 men -- 480 chairs -- 3 days (take 20 chairs x 24= 480)
24 men -- 480 chairs -- 3days
24 men - 300 chairs -- x days
24 men -- 300 chairs - 48 days (480 divide by 300 is 1.6, so i take 3 x 1.6= 4.8)
however, the answer given is 7.5 days.
question 2
5(x-y)^2 - 5x + 5y
= 5(x-y)(x+y) - 5(x+y)
= err then i kind of have no idea how to continue this. help >_<
question 3
Given that y varies directly as t and inversely as the square of x, and y=5 when t=2 and x=4... express y in terms of t and x.
y=kt y= 1/x^2
5=k(2) y= k/x^2
5/2=k 5=k/4^2
* so y= 5/2 t 5=k/16
80=k
* so y= 80/x^2
combining both together:
y= (80/x^2) x ((5/2) t) (and then multiply etc. to this answer:)
y+ 200/x^2 t
so yeah my question is: are my steps + answer for this question correct? i don't have the sample answers with me, so it wld be great if someone can help point out my mistake.
thanks everyone ^_^
Originally posted by lolaminx:i am back , again, and while revising, i came across a couple of questions and i need some clarification:
question 1
If 4 men can make 80 chairs in 12 days, how long will 24 men take to make 300 chairs?
My steps:
4 men --- 80 chairs -- 12 days
1 man -- 20 chairs -- 3 days (take 80 divide by 4 to get 20)
24 men -- 480 chairs -- 3 days (take 20 chairs x 24= 480)
24 men -- 480 chairs -- 3days
24 men - 300 chairs -- x days
24 men -- 300 chairs - 48 days (480 divide by 300 is 1.6, so i take 3 x 1.6= 4.8)
however, the answer given is 7.5 days.
question 2
5(x-y)^2 - 5x + 5y
= 5(x-y)(x+y) - 5(x+y)
= err then i kind of have no idea how to continue this. help >_<
question 3
Given that y varies directly as t and inversely as the square of x, and y=5 when t=2 and x=4... express y in terms of t and x.
y=kt y= 1/x^2
5=k(2) y= k/x^2
5/2=k 5=k/4^2
* so y= 5/2 t 5=k/16
80=k
* so y= 80/x^2
combining both together:
y= (80/x^2) x ((5/2) t) (and then multiply etc. to this answer:)
y+ 200/x^2 t
so yeah my question is: are my steps + answer for this question correct? i don't have the sample answers with me, so it wld be great if someone can help point out my mistake.
thanks everyone ^_^
4 men make 80 chairs in 12 days
1 men make 20 chairs in 12 days
1 men make 5 chair in 3 days
24 men make 120 chairs in 3 days
24 men make 40 chairs in 1 day
24 men make 300 chairs in 7.5 days
5(x-y)^2 - 5x + 5y
5(x-y)^2 + (-5x + 5y)
5(x-y)^2 - 5(x-y)
5 [ (x-y)^2 - (x-y)]
5(x-y) [ (x-y) -1]
Like you said it is a variation question.
The 2 variables are number of chairs and man/days.
Let chair be x and Mandays be y
More mandays = more chair. Thus direct variation.
y varies directly as x.
y = kx
When x = 80, y = 48
48= 80k
k = 0.6
y = 0.6x
When x = 300 y = 24a
24a = 0.6(300)
a = 7.5
1]
4 men --- 80 chairs -- 12 days
NOTE: men inversely proportional to number of days,
men directly proportional to number of chairs.
So let's do it step by step (:
4 men -- 80 chairs -- 12 days
24 men -- 80 chairs -- 2 days
24 men -- 300 chairs -- 7.5 days (1 day -> 40 chairs)
2]
Do they mean factorise? If yes:
5(x-y)^2 - 5x + 5y
= 5(x-y)(x-y) - 5x + 5y
= 5(x-y)(x-y) - 5(x-y)
= [5(x-y)] [(x-y) - 1]
= (5x - 5y)(x - y - 1)
NOTE: (x-y)^2 is not equals to (x-y)(x+y).
3]
y = kt
5 = k(2)
k = 5/2
y = (5/2)t
y = k/(x^2)
5 = k/(4^2)
5 = k/(16)
k = 80
y = 80/x^2
y^2 = (5/2)t * 80/x^2
y = plus/minus square root [(5/2)t * 80/x^2]
y = plus/minus square root (200t/x^2)
You were careless as you times the two y together but you didnt do it to your y^2.
thanks everyone!
hi iampebble... so that means since (x-y)^2 equals to = (x-y)(x-y)... this applies to every algebra questions pertaining to such?
so that means it is only that for eg. (x^2 - 4) is (x+2)(x-2) right?
Originally posted by lolaminx:hi iampebble... so that means since (x-y)^2 equals to = (x-y)(x-y)... this applies to every algebra questions pertaining to such?
so that means it is only that for eg. (x^2 - 4) is (x+2)(x-2) right?
There are 3 general equations you have to take note of :
1) (a+b)^2 = (a+b)(a+b) = (a^2 + 2ab + b^2)
2) (a-b)^2 = (a-b)(a-b) = (a^2 - 2ab + b^2)
3) (a^2 - b^2) = (a+b)(a-b)
=) As long as you practise more you will get the feel of it and they will be a breeze to you in no time! And yes (x^2 - 4) is (x+2)(x-2), because x = a, and 4 = 2^2, which means b = 2. =)