Question

Trying to help my daughter with her homework...
The word problem is...

The ratio of Bill's money to Henry's money was 5:6. After Bill spent $800.00 on a TV set, the ratio became 1:2. How much money did Henry have?

Thx!

Answer 1

let b be the amount of money Bill originally had. let h = amount of money Henry has.
then originally, 5:6 <=> b:h so \[\frac{5}{6}=\frac{b}{h}\Rightarrow h=\frac{6}{5}b\]

after Bill bought the TV we have (b-800):h <=> 1:2 so \[\frac{1}{2}=\frac{b-800}{h}\Rightarrow h=2b-1600 \Rightarrow 2b-h=1600\]
and because \[ h=\frac{6}{5}b \Rightarrow 2b- \frac{6}{5}b=1600\]
solve for b.

Answer 2

She is in the 5th grade and has not done this type of math yet... is there a simpler formula?

Answer 3

5:6 goes to 1:2 = 3:6 after spend $800 so $800 = 2/5 of Bill's money

Answer 4

either way you get the same answer.