Substitution statement

[Thank you Sal]

Statement: Since AB = 1/3 BC, and AC = AB + BC, we can conclude that AB = 1/4 AC
but I cant get to that conclusion
my atempt: (isolate BC) AC = AB + BC -> AC/AB = BC (now substitute) AB = 1/3 AC/AB -> 2AB= AC/3 -> AB AC/3/2 -> AB = 2AC/3
I presume I must be doing something wrong

 

[Pedja]

Hi. We have [imath]BC=AC-AB[/imath]

 

[Harry_the_cat]

AB = 1/3 AC/AB -> 2AB= AC/3 This bit is incorrect. I'm assuming that AB etc are lengths? It should be ^2 on LHS rather than x2.
But that doesn't help solve the problem anyway.

 

[Dr.Peterson]

View attachment 30129
Statement: Since AB = 1/3 BC, and AC = AB + BC, we can conclude that AB = 1/4 AC
but I cant get to that conclusion
my atempt: (isolate BC) AC = AB + BC -> AC/AB = BC (now substitute) AB = 1/3 AC/AB -> 2AB= AC/3 -> AB AC/3/2 -> AB = 2AC/3
I presume I must be doing something wrong

One way to approach this would be to change the fractions around. If AB = 1/3 BC, then BC = 3 AB. And if AC = AB + BC, then AC = AB + 3 AB. Can you see the way from there?

You could even think visually, since clearly the idea is that A, B, and C are on a line in that order. If AB = 1/3 BC, we can draw

A---B---+---+---C

Do you see the implication?

 

[Steven G]

Since AB = 1/3 BC, then 3AB = BC
Now just replace 3*AB for BC in AC = AB + BC and then solve for BC.

Post back with your work.

 

[Thank you Sal]

AB = 1/3 BC
3AB = 1BC (multiply both sides by 3)
AC = AB + BC
AC = AB + 3AB (substitute)
AC = 4AB
1/4 AC = AB (divide both sides by 4)

Do you see the implication?

since line AB + BC = AC and AB is 1/3 of BC -> AB BC BC BC = AC AC AC AC or A-----------B---C = A---------------C (without point B)

Thank you all for helping once again

side note: Im impressed you could visualize the problem even without me posting it by its entirety ( wich was my mistake I wont do it again ) ´´Post the complete text of the exercise´´ - Ted

 

[Dr.Peterson]

side note: Im impressed you could visualize the problem even without me posting it by its entirety ( wich was my mistake I wont do it again ) ´´Post the complete text of the exercise´´ - Ted

So, out of curiosity, can you show us the whole problem now, maybe as an image? And tell us the context?

 

[Thank you Sal]

Of course

Its an exercise from khan academy about dividing line segments
-
find the ratio of AB to AC -> AB = 1/4 AC
multiply that by delta x and y of A and C 1/4 * -4 , 1/4 * -8 -> -1 -2 then add that to point A 6-1 , 1-2 -> 5, 1 and youre done.
at the time I was having a little bit of problem understanding all of this and uncommonly the khan academy explanation was not helping so I thought my only option left was to get help here although eventually with some time admittedly I did get it trough khan academy.

 

[Dr.Peterson]

Of course
View attachment 30145
Its an exercise from khan academy about dividing line segments
-
find the ratio of AB to AC -> AB = 1/4 AC
multiply that by delta x and y of A and C 1/4 * -4 , 1/4 * -8 -> -1 -2 then add that to point A 6-1 , 1-2 -> 5, 1 and youre done.
at the time I was having a little bit of problem understanding all of this and uncommonly the khan academy explanation was not helping so I thought my only option left was to get help here although eventually with some time admittedly I did get it trough khan academy.

Ah! So the part you are asking about is just one small step that he assumed you could see without much explanation. The context makes it clearer what level of thinking is expected.

This can be thought of as a familiar idea about ratios, closely related to my picture. If the ratio of two parts is 1:3, then the parts are respectively 1/4 and 3/4 of the whole, which you find by adding the parts, 1 + 3 = 4 and using that as the denominator. He may be assuming some such thinking.

 

[Thank you Sal]

If the ratio of two parts is 1:3, then the parts are respectively 1/4 and 3/4 of the whole, which you find by adding the parts, 1 + 3 = 4 and using that as the denominator

How to make someone understand the ratio concept instantly ↑

 

[Dr.Peterson]

How to make someone understand the ratio concept instantly ↑

There is an old saying: There is no royal road to mathematics. You need to do it enough (paying close attention to details) to make it natural. No one can force it into your mind. But I think drawing pictures helps a lot. Or playing with physical objects.