The perimeter of a triangle is 45 centimeters. The longest side is 5 centimeter(s) less than the sum of the other two sides. Twice the shortest side is 4 centimeters less than the longest side.
Find the lengths of each side of the triangle.
The length from the shortest to longest are_, _, and _ centimeters?

- anonymous

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- katieb

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- anonymous

The information you're given allows you to set up three equations in three unknowns. Name the sides as:
l = longest
s = shortest
a = remaining side
The perimeter is 45, which is the sum of the lengths of the sides, so\[l+s+a=45\]is one equation. You're told that the longest side is 5 LESS than the SUM of the other two sides, so\[l=a+s-5\]and finally, TWICE the shortest side equals 4 LESS than the longest, namely,\[2s=l-4\]

- anonymous

You have three linear equations in three unknowns, so you can solve the system exactly.

- anonymous

Lol. Ok, so what;s the answers though?

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## More answers

- anonymous

i like the way you explain it though...

- anonymous

Well, you have to do some substituting. Take any one of you equations to begin with. Use the second to plug into the third to eliminate for l. So,\[2s=(a+s-5)-4=a+s-9 \rightarrow a=s+9\]

- anonymous

Let me sort it.

- anonymous

.......

- anonymous

It's fast to do on paper but a pain to do online.

- anonymous

tell me about it...

- anonymous

If you sub. the equation for l (second one) into the first, you should get\[(a+s-5)+s+a=45 \rightarrow s+a=20\]

- anonymous

If you sub the same second equation for l into the third, you get\[2s=(a+s-5)-4 \rightarrow a-s=9\] (forget the equation I solved at the very beginning, I stuffed the sign).

- anonymous

You now have \[a+s=20\]and\[a-s=9\]

- anonymous

If a=9+s from the second equation here, then putting it into the first, you get\[(9+s)+s=20 \rightarrow 2s=11 \rightarrow s=\frac{11}{2}\]

- anonymous

lol..this is a monster!

- anonymous

Which means, from any of the two equations involving a and s above, for a,\[a=9+s=9+\frac{11}{2}=\frac{29}{2}\]

- anonymous

Now from your perimeter equation, you can solve for l:\[l=45-a-s=45-\frac{29}{2}-\frac{11}{2}=25\]

- anonymous

You're done.

- anonymous

Well, I am...

- anonymous

so it's how many centimeters each?

- anonymous

Just look through -
l = 25 cm
s = 5.5 cm
a = 14.5 cm

- anonymous

crap

- anonymous

crap what?

- anonymous

The correct answers were 8,17, and 20! :(

- anonymous

Now it reformulates a new, but similar problem for me to solve.

- anonymous

Now it's......

- anonymous

- anonymous

Yes a mistake was made. You need to check everything once it's solved but putting it back into the equations.

- anonymous

its the same one!
never had that happen before.

- anonymous

so what would be the "mistake free" answer? :)

- anonymous

Well, if it's the same question, you already have the answers - you just posted them!

- anonymous

LOL......DUH!

- anonymous

I didn't even think of that.

- anonymous

Sigh......long day.

- anonymous

Want a shot at another?

- anonymous

Depends, if you give me back my fan point ;)

- anonymous

Fair enough!

- anonymous

Do you have the question?

- anonymous

Yeah, it's a beast....
one sec.....

- anonymous

In a certain year out of pocket expenses for an elderly person in poor health were 3353 more than for an elderly person in good health. Combined out of pocket expenses for one person in poor health and one person in good health was 6677 find the our of pocket expenses for each type of person.
Out of pocket expenses for a person in poor health was....
Out of pocket expenses for a person in good health was....

- anonymous

phew!

- anonymous

Do you just want the answer?

- anonymous

Did you take my point off again? lol

- anonymous

lol...me? Nooooooo! Why would you ask that?! ;)

- anonymous

poor health person = 5015
good health person = 1662

- anonymous

Yes.....I was holding it hostage until you returned. It's back.

- anonymous

Ok......now enlighten me how you got it so darn fast! I have a friend on here that is taking the same class and I want to help her too.

- anonymous

She is Kelley29 I think..

- anonymous

poor health out-of-costs = p
good health out-of-costs = g
Information says
p = 3353 + g
p + g = 6677
Solve the two. First is p=3353 + g so sub. into second to get rid of p:
(3353 + g) = 6677

- anonymous

.............

- anonymous

g=6677-3353=1662

- anonymous

p=3353+ g = 3353 + 1662 = 5015

- anonymous

Ok what her numbers are poor health=3334, good health=6596

- anonymous

she just gave me that, and I have no idea what that formula is you just gave me.....unfortunately.
I will tell her to give you a POINT!

- anonymous

you're a star

- anonymous

Whats tha t mean?

- anonymous

It just means I appreciate your offer to get your friend to give me a point.

- anonymous

Lol, i'ts the least I can do!

- anonymous

SO what is it?

- anonymous

what is what?

- anonymous

her answer! lol

- anonymous

U need more info?

- anonymous

I don't have her question - what's her login name?

- anonymous

Just give me a second, I'm just helping someone else too.

- anonymous

Same questions!
Hers is Kelley29

- anonymous

Ok n/m some dude just got it for her.

- anonymous

But...we have more. At least a coupla more.

- anonymous

Kelly29 is being helped by blexting.

- anonymous

He/she does a good job.

- anonymous

Ok, well I have more...

- anonymous

Translate to a system of equations, but do not solve.
An non toxic floor wax can be made from lemon juice and food grade linseed oil.
The amount of oil should be twice the amount of lemon juice. How much of each ingredient is needed to make 42 ounces of floor wax?
Let x represent the number of ounces of lemon juice and y the number of ounces of linseed oil.
Complete the system of equations.
y=
x+y=

- anonymous

It's absolutely ridiculous!

- anonymous

...........

- anonymous

y=2x
x+y =42
------------------------------------------------------
You're told you need 2 times as much x as y (2 times as much lemon juice as linseed oil).
You also know that the total weight, x + y, should be 42 oz.

- anonymous

ANd AGAIN........you got it right!

- anonymous

last one here for the night.....i promise.........

- anonymous

If a plane can travel 480 miles per hour with the wind, and 380 miles per hour against the wind, find the speed of the plan without a wind and the speed of the wind.
The speed of the plan in still air is _miles per hour.

- anonymous

It's 430 miles per hour

- anonymous

Ok........the speed of the WIND is?

- anonymous

50, sorry, forgot

- anonymous

50mph?

- anonymous

Ok, can you PLEASE help my friend now.....you rock, and these other guys suck apparently! I will tell her to rock your points! :,)

- anonymous

Thank you very much by the way......I really do appreciate your help.

- anonymous

Thanks for the praise. I'll see what I can do. I promised someone else I'd help him and he's been waiting. If kelley29 is still around when I'm done, I'll help.

- anonymous

I understand. You're the best! I hope to see you on here for the next 4 weeks or so.

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