Word Problem

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Hockeyman

Junior Member
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Dec 8, 2005
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The measure of two angles are in the ratio 5:3. The measure of the larger angle is 30 greater than half the difference of the angles. Find the measure of each angle. There are two pairs of angles that will work as answers.

Now i'm stuck.

here are my variables:

x= large angle

y= smaller angle

I thought mabe you could solve this problem using a system of equations, so i tried to create an equation:

(x-y)/2 + 30 = x

Is this correct? I still don't know the other equation. Or the other way to get the other set of angles. Any help would be greatly appreciated. :D
 
since the ratio of the angles is 5:3 ...

let the large angle = 5x
small angle = 3x

now ... try again and see if that doesn't make the problem much easier.
 
Hockeyman said:
The measure of two angles are in the ratio 5:3. The measure of the larger angle is 30 greater than half the difference of the angles. Find the measure of each angle. There are two pairs of angles that will work as answers.
Now i'm stuck.
here are my variables:
x= large angle
y= smaller angle
I thought mabe you could solve this problem using a system of equations, so i tried to create an equation:
(x-y)/2 + 30 = x
Is this correct? I still don't know the other equation. Or the other way to get the other set of angles. Any help would be greatly appreciated.

x = large and y = small

y/x = 5/3

y = (y - x)/2 + 30

Can you take it from here?
Click to expand...
 
I'm not sure that would work. I think since you are trying to find a ration you could try and put it into fraction form.

like:

x/3 = y/5

because you have the large angle (x) to the ratio of three(the smaller angle), and that equals the smaller angle which is the ratio to five (the larger angle).

I'm not sure if that is right, any feedback?
 
... ever heard of working smart and not hard? why do you insist on using two variables?

large angle = 5x
small angle = 3x
(that's in a ratio of 5:3, isn't it?)

The measure of the larger angle is 30 greater than half the difference of the angles.

5x = 30 + (5x - 3x)/2
5x = 30 + x
4x = 30
x = 7.5

large angle = 5x = 5*7.5 = 37.5 degrees
small angle = 3x = 3*7.5 = 22.5

you can check the result yourself.
 
Ok both ways work, and you get the same answer, now there is still one more set of angles to find. Anyone know how to find those angles?
 
depends on how the difference is taken ...

5x = 30 + (3x - 5x)/2

5x = 30 - x

6x = 30

x = 5

5x = 25

3x = 15
 
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