Random Geometric question

[Akumaz]

i was asked to help with a grade 11 math question, and i can not figure it out.... so beyond, help a brother out!

geometric question

if the first term is 8, and the sum of the 3 terms is 87,
what are the other 2 terms? and what is the ratio?

i trial and error-ed the answer to r=2.5
but there has got to be a better way to do it through some sort of formula, i looked at all the formulas that were given, but i cant use any as i have 2 variables...
unlesss, i am suppose to use 2 formulas and 2 variables... hm.. i will try it in the mean time,
anyone who knows how to solve this, help me out, thanks~~!!

[DeeK]

PIE-ARR-Squared. Pirates are fun.

[DeeK]

http://cdn.smosh.com/sites/default/files/bloguploads/uht-23.jpg

[Mar]

y=mX+b

If you have 2 variables, it has to be solved by plotting it on a graph. You can't solve for any one variable.

[kaput]

.

[Sal0]

Since no one else answered...here is my best guess. The question does seem to be worded funny.
8+X+Y=87

X=-Y+79
Y=-X+79
and as per Mar's formula M = -1 which is the ratio.

[jwslam]

Originally posted by Sal0
8+X+Y=87

Probably something like that
where Y=2x

ratio is X/8

My answer: Ratio is 79/24

[lilmira]

Can people ask a question properly nowadays?

My answer is b.

[revelations]

sounds like you need to solve it with the quadratic formula.

[98brg2d]

You are not clear on the actual problem (as noted above). If you want an answer that makes no assumptions you need to provide the entire problem.

Equations:

8 +x + y = 87 (known)
8/x = r (???assumption based on what you said about ratios)
x/y = r (???again assumption)

therefore x = 8/r, y = 8/r²
then 8 + 8/r + 8/r² = 87
or 8r² + 8r + 8 = 87r²
or 79r² - 8r - 8 = 0

you would then need to use a root solver or graphing tool (assumption that this is the intent since it is grade 11 and they should be learning about graphing calculators).

The roots are 0.3728587863, -0.2715929635; however, only the positive root satisfies the original (known) equation. Both roots are irrational. Since all the coefficients in the original equation are rational, I would expect that the "ratio" stuff you are talking about should lead to a rational solution (not necessarily the case though).

If you clarify what you meant by "ratio" you will get a better answer.

[Akumaz]

Thanks for the replys, i just realized i indeed messed up the question, SORRY!

it is suppose to be

if the first term is 8, and the sum of the 3 terms is 78,
what are the other 2 terms? and what is the ratio?


so basically it means that:

8,x,y <-- 3 terms total x=8(r) y=8(r)(r)
8+8(r)+8(r)(r)=78 <-- not 87 as i typed it in wrong

so with trial and error, i found r to be 2.5
i can probably graph it and find it, but the point is not to use a graphing calculator, but through the geometric sequence formulas

[lilmira]

Ok I'll try.

8r^2 + 8r + 8 = 78
8r^2 + 8r -70 = 0
4r^2 + 4r -35 =0
(2r)^2 + 4r - (5x7) =0
(2r+7)(2r-5)=0

something like that? Haven't done this for many many years.


Oops, fixed a typo.

[Akumaz]

ya neither, its been like 6 -7 years since high school days..
i was just asked that question and i couldnt answer it...
now its bugging me haha
it seems like the only way to solve is through graphing..
hm.. ..

thanks for everyones help!

[jwslam]

Originally posted by Akumaz
it seems like the only way to solve is through graphing..
hm.. ..

Quadratic equation

8r²+8r+(8-78)=0

to form
ax²+b+c=0

where x=r
a=8
b=8
c=-70

use
http://www.crewtonramoneshouseofmath.com/images/quad_eq.gif

Ans: r=2.5, -3.5

Therefore the terms can be [20,50] or [-28,98]


Originally posted by lilmira
Ok I'll try.

8r^2 + 8r + 8 = 78
8r^2 + 8r -70 = 0
4r^2 + 4r -35 =0
(2r)^2 + 4r - (5x7) =0
(2r+7)(2r-5)=0

something like that? Haven't done this for many many years.


Oops, fixed a typo.
This works as well because
(2r+7)=0 gives r=-3.5 and
(2r-5)=0 gives r=2.5