SOLUTION: Diana used 1/3 of his salary for food and keep 1/4 of remaining as saving. After that 50% of the remaining is used to pay rent. determine what fraction of his salary is left.

Algebra ->  Numeric Fractions Calculators, Lesson and Practice -> SOLUTION: Diana used 1/3 of his salary for food and keep 1/4 of remaining as saving. After that 50% of the remaining is used to pay rent. determine what fraction of his salary is left.       Log On


   

Question 1132317: Diana used 1/3 of his salary for food and keep 1/4 of remaining as saving. After that 50% of the remaining is used to pay rent. determine what fraction of his salary is left.
Found 2 solutions by Theo, ikleyn:
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
let x represent the salary.

1/3 * x is used for food.

x - 1/3 * x = 3/3 * x - 1/3 * x = 2/3 * x.

2/3 * x remains.

1/4 * 2/3 * x = 2/12 * x = 1/6 * x is used for saving.

2/3 * x - 1/6 * x = 4/6 * x - 1/6 * x = 3/6 * x = 1/2 * x.

1/2 * x remains.

1/2 * 1/2 * x = 1/4 * x is used for rent.

1/2 * x - 1/4 * x = 2/4 * x - 1/4 * x = 1/4 * x.

1/4 * x remains.

that's your solution.

to summarize:

1/3 * x is used for food.
1/6 * x is used for saving.
1/4 * x is used for rent.
1/4 * x remains.

1/3 * x + 1/6 * x + 1/4 * x + 1/4 * x equals 4/12 * x + 2/12 * x + 3/12 * x + 3/12 * x which is equal to 12/12 * x which is equal to x.

all salary is accounted for.





Answer by ikleyn(52780) About Me  (Show Source):
You can put this solution on YOUR website!
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            I used to think that Diana is the woman's name;  but it looks like the author of this post thinks and uses it differently.