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January 9th, 2011, 06:54 AM   #1
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Ratios

How do I solve this?

In an election for senior class president, Alice received 30 votes more than David. If the ratio of the number of votes Alice received to the number of votes David received was 8 to 7, how many votes did David receive?

I have two unknowns: # of votes David receives = 7/15 times some number to give 30 + some number.
MathematicallyObtuse is offline  
 
January 9th, 2011, 07:27 AM   #2
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Re: Ratios

If the ratio is 8:7 doesn't it just mean that David received 7*30 votes, which is 210? Or am I missing something silly

Or using simultaneous equations:

a - 30 = d
7/8a = d

8a - 240 = 8d
7a = 8d

a - 240 = 0
a = 240
d = 210
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January 9th, 2011, 07:45 AM   #3
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Re: Ratios

Hello, Chimoo!

Quote:
If the ratio is 8:7, doesn't it just mean that David received 7x30 votes, which is 210 ?
Or am I missing something silly? [color=beige] . [/color] [color=blue] no![/color]

Absolutely correct!

A terrific "eyeball" solution!

soroban is offline  
January 9th, 2011, 08:07 AM   #4
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Re: Ratios

Quote:
Originally Posted by Chimoo
If the ratio is 8:7 doesn't it just mean that David received 7*30 votes, which is 210? Or am I missing something silly

Or using simultaneous equations:

a - 30 = d
7/8a = d

8a - 240 = 8d
7a = 8d

a - 240 = 0
a = 240
d = 210
Delightful! I wouldn't have seen that in a million years! Thank you
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