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16 Jul 2010, 13:22
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Can someone show me how to solve this algebraically
Lisa spend 3/8 of her pay on rent and 5/12 on food. her roommate earns twice as much and spend 1/4 on rent and 1/2 on food. If the two women donate all remaining money to charity, what percentage of their combined income do they donate
Lisa spend 3/8 of her pay on rent and 5/12 on food. her roommate earns twice as much and spend 1/4 on rent and 1/2 on food. If the two women donate all remaining money to charity, what percentage of their combined income do they donate
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19 Jul 2010, 08:55
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Lisa spend \(=\frac{3}{8}+\frac{5}{12}=\frac{9+10}{24}=\frac{19}{24}\) => amount left \(= 1-\frac{19}{24}=\frac{24-19}{24}=\frac{5}{24}\)
roommate spend \(=\frac{1}{4}+\frac{1}{2}=\frac{1+2}{4}=\frac{3}{4} = >\) => amount left \(= 1-\frac{3}{4}=\frac{4-3}{4}=\frac{1}{4}\)
Let Lisa earned X => roommate earns 2*X => total amount left \(= \frac{5}{24}*X+\frac{1}{4}*2*X=\frac{5+12}{24}*X=\frac{17}{24}*X\)
thus percentage of their combined income \(= \frac{\frac{17}{24}*X}{3*X}=\frac{17}{24*3}=23.61%\)
roommate spend \(=\frac{1}{4}+\frac{1}{2}=\frac{1+2}{4}=\frac{3}{4} = >\) => amount left \(= 1-\frac{3}{4}=\frac{4-3}{4}=\frac{1}{4}\)
Let Lisa earned X => roommate earns 2*X => total amount left \(= \frac{5}{24}*X+\frac{1}{4}*2*X=\frac{5+12}{24}*X=\frac{17}{24}*X\)
thus percentage of their combined income \(= \frac{\frac{17}{24}*X}{3*X}=\frac{17}{24*3}=23.61%\)
19 Jul 2010, 13:43
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same explanation as - vittarr.
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