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At a bakery, Tom normally earns x dollars per hour of the first n hours of the day. For each hour he works in excess of n hours on a given day, he is paid 1.375 times his regular rate. If Tom decides to start working over time, what is the ratio of over time hours to regular time hours required to double his daily income?
  • a)
    7 : 10
  • b)
    375 : 100
  • c)
    100 : 375
  • d)
    11 : 8
  • e)
    8 : 11
Correct answer is option 'E'. Can you explain this answer?
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At a bakery, Tom normally earns x dollars per hour of the first n hour...
Understanding Tom's Regular and Overtime Pay
To solve the problem, we need to analyze Tom's earnings based on his regular and overtime hours.
Regular Earnings
- Tom earns x dollars/hour for the first n hours.
- His total earnings for regular hours:
Regular Earnings = n * x
Overtime Earnings
- For every hour worked beyond n hours, he earns 1.375x dollars/hour.
- If he works h hours of overtime, his earnings from overtime:
Overtime Earnings = h * 1.375x
Total Earnings in a Day
- The total earnings for a day where he works n regular hours and h overtime hours is:
Total Earnings = n * x + h * 1.375x
Doubling His Income
- To double his income, Tom needs:
Total Earnings = 2 * (n * x)
- Setting up the equation:
n * x + h * 1.375x = 2n * x
Simplifying the Equation
- Dividing the entire equation by x (assuming x ≠ 0):
n + 1.375h = 2n
- Rearranging gives:
1.375h = 2n - n
1.375h = n
Finding the Ratio
- Isolating for h gives:
h = n / 1.375
- To express the ratio of h (overtime hours) to n (regular hours):
h/n = 1/1.375 = 8/11
Thus, the ratio of overtime hours to regular time hours required to double his daily income is 8:11. Hence, the correct answer is option E.
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At a bakery, Tom normally earns x dollars per hour of the first n hours of the day. For each hour he works in excess of n hours on a given day, he is paid 1.375 times his regular rate. If Tom decides to start working over time, what is the ratio of over time hours to regular time hours required to double his daily income?a)7 : 10b)375 : 100c)100 : 375d)11 : 8e)8 : 11Correct answer is option 'E'. Can you explain this answer?
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