Question

Mr. Johnson was to earn Pounds 300 and a free holiday for seven weeks. He worked for only 4 weeks and earned Pounds 30 and a free holiday. What was the value of the holiday?

Answer 1

Hint: In the question, we are given that Mr. Johnson gets 300 Pounds and a holiday if he works for 7 weeks but he works for only 4 weeks and gets 30 Pounds and a free holiday. So, we can find out his earnings per week from the given equation which will help us find the earnings of 4 weeks, and by comparing it with the given earnings of 4 weeks, we can find out the value of the free holiday.

Complete step-by-step answer:
Let the value of the holiday be x.
On working for 7 weeks, Mr. Johnson earns $ = 300\;pounds + x $
On working for 1 week, Mr. Johnson earns $ = \dfrac{{300\;pounds + x}}{7} $
On working for 4 weeks, Mr. Johnson earns $ = 4 \times \dfrac{{300\;pounds + x}}{7} $
And, we are given that Mr. Johnson gained 30 pounds and a free holiday on working for 4 weeks
That can be written as $ 30\;pounds + x $ .
Now, on comparing the obtained equation with the given equation, we get –
 $
  \dfrac{4}{7} \times (300 + x) = 30 + x \\
  1200 + 4x = 210 + 7x \\
  7x - 4x = 1200 - 210 \\
  3x = 990 \\
  x = 330 \;
  $
Thus, the value of the free holiday is 330 pounds.
So, the correct answer is “330 pounds”.

Note: The holiday remains the same in both durations whereas the amount of money given to him changes, so it is actually the value of holiday that decides the amount of money Mr. Johnson earns. Thus it is important to find its value. We have two situations that can be written in the form of equations and the value of one unknown quantity can be easily obtained in such cases.