Ratio question: If a:b is 2:7 and a:b+8 is 2:5, find a and b.

[rainstar]

Hi, can anyone please help with this....

If a:b is 2:7 and a:b+8 is 2:5, find a and b.

The answer is B = 20 and a=70

I just don't know how to get to the answer. Thank you/

 

[Otis]

a:b is 2:7

answer is B = 20 and a=70

Hi rainstar. Something is wrong with either the exercise statement or that answer. If a=70 and b=20, then the ratio a:b is 70:20 which simplifies to 7:2.

Please check that you've correctly posted everything you've been given.

PS: In math, symbols B and b are not the same, so just use b.

 

[Otis]

If a:b is 2:7 and a:b+8 is 2:5, find a and b.

Hi, again. If we solve the exercise as stated, then a and b are both negative Integers.

If we change a:b to 7:2, then a and b are both fractions with 31 in the denominator.

If we change a:b to 7:2 and change b+8 to b+155, then we get a=70 and b=20.

All of that makes me think somebody gave you the wrong answer. If you would like to use the exercise as stated, then please share how far you get, so we can see what you're trying.

 

[Otis]

Sorry, I keep getting interrupted. Spoiled dogs!

Another possibility is that they gave the correct answer, but they accidently inverted two of the ratios in the exercise statement. You'll get the given answer, if you solve this one:

If a:b is 7:2 and a:b+8 is 5:2, find a and b.

If you don't know how to begin, here's a first step: write the four ratios as fractions, and write both proportions as equations.

a/b = 7/2

a/(b+8) = 5/2

Can you solve the second equation for a? If so, then substitute the result for a in the first equation. That yields a new equation containing only b, which you solve to find b=20.

 

[rainstar]

Thank you so much Otis! Yes, I agree that either the answer is wrong or the ratios are inverted! I inverted the ratios as you suggested in your third post and I do get a=70 and b=20. It does work, but only if it is 7:2 rather than 2:7!

You mentioned in your second post that If we change a:b to 7:2, then a and b are both fractions with 31 in the denominator. How did you get 31?

 

[Otis]

I inverted the ratios as you suggested in your third post … It does work, but only if it is 7:2 rather than 2:7

You inverted both ratios (2:7 and 2:5), yes?
2/7 becomes 7/2
2/5 becomes 5/2

You mentioned … If we change a:b to 7:2, then a and b are both fractions with 31 in the denominator. How did you get 31?

In that experiment, my only change was a:b=7:2 (because the answer implied 70:20). I'd left a:b+8 as the given 2:5.

 

[The Highlander]

Made this just after Post #2 but see it's 'out of date' now that I've logged in (hours later) to post it.

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