A sales representative earns 4 times as much in the the 4th week of January as in each of the other 3 weeks. What part of his income was earned in the 4th week
4/7
To determine the part of the income earned in the 4th week of January, we need to calculate the proportion of the total income that was earned in the 4th week.
Let's assume the income earned in each of the first three weeks is represented by x. According to the given information, the sales representative earns 4 times as much in the 4th week. Therefore, the income in the 4th week is 4x.
The total income earned in January can be calculated by adding up the income earned in all four weeks:
Total income = (Income in 1st week) + (Income in 2nd week) + (Income in 3rd week) + (Income in 4th week)
Total income = (x) + (x) + (x) + (4x)
Total income = 7x
Now, to determine the proportion of the income earned in the 4th week, we divide the income in the 4th week by the total income:
Proportion of income earned in 4th week = (Income in 4th week) / (Total income)
Proportion of income earned in 4th week = (4x) / (7x)
Proportion of income earned in 4th week = 4/7
Therefore, the sales representative earned 4/7 or approximately 57.14% of their income in the 4th week of January.