Ray and Stella are both given jobs by the same company. Ray is to be paid a basic salary of $3000 each month. He will get a raise of $100 after the first month and every month thereafter he will get a raise of $100 more than the preceding month. Stella will be paid a basic salary of $1500 for every half-month. At the end of the first half-month she will get a raise of $25 and for every half-month thereafter she will get a raise of $25 more than the preceding half-month. At the end of the year Stella will have made $______ more than Ray.

Question

Ray and Stella are both given jobs by the same company. Ray is to be paid a basic salary of $3000 each month. He will get a raise of $100 after the first month and every month thereafter he will get a raise of $100 more than the preceding month. Stella will be paid a basic salary of $1500 for every half-month. At the end of the first half-month she will get a raise of $25 and for every half-month thereafter she will get a raise of $25 more than the preceding half-month. At the end of the year Stella will have made $______ more than Ray.

Answer 1

in the nth month, ray gets 3000+100(m-1) = 2900 + 100m

in the nth half-month, stella gets 1500 + 25(n-1) = 1475 + 25n

The year has 12 months and 24 half-months.

during the year,
ray makes 12/2 (2900 + 2900 + 11*100) = $41,400
stella makes 24/2 (1475 + 1475+23*23) = $41,748

Answer 2

To find out how much Stella will have made more than Ray at the end of the year, we need to calculate the total salary earned by both Ray and Stella and then find the difference between the two.

Let's start by calculating Ray's total salary for the year, assuming he receives his raise every month:

Ray's basic salary is $3000 per month.
His raise amount increases by $100 every month.

To calculate Ray's total salary, we need to determine the number of months in a year and the total raise amount he receives.

Since there are 12 months in a year, Ray will receive the raise for 12 - 1 = 11 months.

Now we can calculate the raise amount:
raise_amount = $100 * 11 = $1100

Ray's total salary for the year would be:
total_salary_ray = basic_salary + raise_amount = $3000 + $1100 = $4100

Next, let's calculate Stella's total salary for the year, assuming she receives her raise every half-month:

Stella's basic salary is $1500 for every half-month.
Her raise amount increases by $25 every half-month.

To calculate Stella's total salary, we need to determine the number of half-months in a year and the total raise amount she receives.

Since there are 12 months in a year and 2 half-month periods in a month, there are 12 * 2 = 24 half-months in a year.

Stella will receive the raise for 24 - 1 = 23 half-months.

Now we can calculate the raise amount:
raise_amount = $25 * 23 = $575

Stella's total salary for the year would be:
total_salary_stella = basic_salary + raise_amount = $1500 + $575 = $2075

Finally, we can find the difference between Stella's and Ray's total salaries:
difference = total_salary_stella - total_salary_ray = $2075 - $4100 = $-2025

Since the result is negative, it means that Stella will have earned $2025 less than Ray at the end of the year.