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Lisa spends 3/8 of her monthly paycheck on rent and 5/12
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11 Jan 2023, 03:54
11 Jan 2023, 03:54
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Question Stats:
62% (02:37) correct
37% (03:42) wrong based on 8 sessions
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Lisa spends 3/8 of her monthly paycheck on rent and 5/12 on food. Her roommate, Carrie, who earns twice as much as Lisa, spends 1/4 of her monthly paycheck on rent and 1/2 on food. If the two women decide to donate the remainder of their money to charity each month, what fraction of their combined monthly income will they donate? (Assume all income in question is after taxes.)
Show: ::
17/72
Re: Lisa spends 3/8 of her monthly paycheck on rent and 5/12
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21 Jan 2023, 01:43
21 Jan 2023, 01:43
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Use a common denominator for all the fractions which is 24
The roommate spends as double as $24= $48
Lisa spends
rent 3/8 of 24=9
food 5/12 of 24=10
24-19=5
Carries spends
rent 1/4 of 48=12
food 1/2 of 48=24
48-36=12
Combined they donate 17 out of the total 72
$ 17/72
The roommate spends as double as $24= $48
Lisa spends
rent 3/8 of 24=9
food 5/12 of 24=10
24-19=5
Carries spends
rent 1/4 of 48=12
food 1/2 of 48=24
48-36=12
Combined they donate 17 out of the total 72
$ 17/72
Lisa spends 3/8 of her monthly paycheck on rent and 5/12
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27 Feb 2024, 05:53
27 Feb 2024, 05:53
Since we see only fractions of the salary and no actual numbers for anything in the problem, it is best done by choosing numbers for unknown quantities (such as salary in this case) instead of using variables (to represent salary in this case).
When choosing a number, choose a number which is the LCM of the denominators of fractions to simplify future calculations. Such a number or numbers are called smart numbers.
denominators = \(8, 12, 4, 2\)
LCM (of denominators) = \(24\)
Lisa
Paycheck = \(24\)
Rent = \(\frac{3}{8} \times 24 = 9\)
Food = \(\frac{5}{12} \times 24 = 10\)
Remaining Salary = \(24-9-10 = 5\)
Carrie
Paycheck = \(48\) (twice that of Lisa)
Rent = \(\frac{1}{4} \times 48 = 12\)
Food = \(\frac{1}{2} \times 48 = 24\)
Remaining Salary = \(48-12-24 =12\)
Total Remaining Salary (donated to charity) = \(5 + 12 = 17\)
Total Salary = \(24+48 = 72\)
Fraction of Salary donated to Charity
\(\dfrac{17}{72}\)
When choosing a number, choose a number which is the LCM of the denominators of fractions to simplify future calculations. Such a number or numbers are called smart numbers.
denominators = \(8, 12, 4, 2\)
LCM (of denominators) = \(24\)
Lisa
Paycheck = \(24\)
Rent = \(\frac{3}{8} \times 24 = 9\)
Food = \(\frac{5}{12} \times 24 = 10\)
Remaining Salary = \(24-9-10 = 5\)
Carrie
Paycheck = \(48\) (twice that of Lisa)
Rent = \(\frac{1}{4} \times 48 = 12\)
Food = \(\frac{1}{2} \times 48 = 24\)
Remaining Salary = \(48-12-24 =12\)
Total Remaining Salary (donated to charity) = \(5 + 12 = 17\)
Total Salary = \(24+48 = 72\)
Fraction of Salary donated to Charity
\(\dfrac{17}{72}\)
