Ratio word problems

fruityfreckles

New member
Joined
Jan 18, 2011
Messages
1
Hey!
So, I'm trying to work out these ratio word problems.... and I'm a bit stuck.
The word problem looks like this:
"Two numbers are in the ratio 3:7. If 1 is added to the smaller problem and 7 is added to the larger,
they will be in the ratio 1:3. Find the numbers.

To find the answer for the first number (3) I did this: (not sure if this is right...)
3x + 1 = 1x
2x = -1
x = -2
3 times -2 would be -6... right?
Or do you take -2 away from the original number, 3?

Do I do the same process (or is this completely wrong?) to find the next number (7)?
When I tried working out the second half of the problem... it looked completely wrong:
7x + 7 = 3x
4x = -7
x = 1 3/4
Yeah... so not right!

Any idea how to work this ratio problem out?
Thanks! :D
 
I'll start you off:

The two numbers are \(\displaystyle 3x\) and \(\displaystyle 7x\) for some \(\displaystyle x\) (this is what it means to be in the ratio \(\displaystyle 3:7\))

\(\displaystyle \frac{3x+1}{7x+7}=\frac{1}{3}\).

Make sure you understand where this equation comes from.
 
So, I'm trying to work out these ratio word problems.... and I'm a bit stuck.
The word problem looks like this:
"Two numbers are in the ratio 3:7. If 1 is added to the smaller problem and 7 is added to the larger,
they will be in the ratio 1:3. Find the numbers.

To find the answer for the first number (3) I did this: (not sure if this is right...)
3x + 1 = 1x
2x = -1
x = -2
3 times -2 would be -6... right?
Or do you take -2 away from the original number, 3?

Do I do the same process (or is this completely wrong?) to find the next number (7)?
When I tried working out the second half of the problem... it looked completely wrong:
7x + 7 = 3x
4x = -7
x = 1 3/4
Yeah... so not right!

Any idea how to work this ratio problem out?

Given x/y = 3/7 or x = 3y/7.

Given (x + 1)/(y + 7) = 1/3

Substitiuting, [(3y/7) + 1]/(y + 7) = 1/3

Multiplying out and simplifying, y = 14 and x = 6.
 
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