Question

In a certain month, Mason spent 1/6 of his salary in the first three days and $800 in the following ten days and after that he was left with half of his salary. What was Mason’s salary in dollars for that month?

Answer 1

Answer:   $2400

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Explanation:

x = Mason's salary in dollars for that month

x/6 = one-sixth of his salary

x/6+800 = total amount spent (the x/6 dollars and $800 combined)

In total, he spent half his salary. This means he spent x/2 dollars for the month overall.

Set the two items equal to one another. Solve for x.

x/6 + 800 = x/2

6(x/6 + 800) = 6*(x/2) ... see note at the bottom of the page

x+4800 = 3x

4800 = 3x-x

4800 = 2x

2x = 4800

x = 4800/2

x = 2400

His monthly salary is $2400

1/6 of this is (1/6)*2400 = 2400/6 = 400 dollars. Add on the $800 he also spent to get a total of 400+800 = 1200 dollars spent, which is exactly one half of the $2400. The answer is confirmed.

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Note: I multiplied both sides by 6 to clear out the fractions. The value 6 is the LCD in this case.