Ratio proportion

[bala]

The question is :

An IT department of fewer than 15 people hires coders and system analysts... Coders are paid 55000 per year on average while system analysts are paid 45000 on average yearly. What is the ratio of coders to system analysts

1) if two coders were made system analysts the yearly payroll for IT department will be 535000

2) if the system analysts salaries were reduced by one-third and coder salaries were increased to 58000, the department would save 57000 in yearly payroll

The answer given is Statement 1 & 2 alone are sufficient... How???

 

[stapel]

The question is :

An IT department of fewer than 15 people hires coders and system analysts... Coders are paid 55000 per year on average while system analysts are paid 45000 on average yearly. What is the ratio of coders to system analysts

1) if two coders were made system analysts the yearly payroll for IT department will be 535000

2) if the system analysts salaries were reduced by one-third and coder salaries were increased to 58000, the department would save 57000 in yearly payroll

The answer given is Statement 1 & 2 alone are sufficient... How???

The "question" asks for the ratio of coders to analysts. How is the "answer" anything other than a number (or ratio)?

Please reply with the full text of the exercise and its instructions. Thank you!

 

[HallsofIvy]

The question is :

An IT department of fewer than 15 people hires coders and system analysts... Coders are paid 55000 per year on average while system analysts are paid 45000 on average yearly. What is the ratio of coders to system analysts

Call the numbers of coders "c" and the number of analysts "s". The annual payroll is 55000c+ 45000s.

1) if two coders were made system analysts the yearly payroll for IT department will be 535000

If the number of coders were c- 2 and the number of system analysts were s+ 2 the payroll would be 55000(c- 2)+ 45000(s+2)= 535000.

2) if the system analysts salaries were reduced by one-third and coder salaries were increased to 58000, the department would save 57000 in yearly payroll

So if the systems analyst's salaries were 45000- (1/3)45000= (2/3)45000= 30000 and the coder's salaries were 58000, the payroll would be 58000c+ 30000s and that would be 57000 less than the previous 55000c+ 45000s: 58000c+ 30000s= 55000c+ 45000c- 57000.

Solve those two equations for s and c.

The answer given is Statement 1 & 2 alone are sufficient... How???

It seems very strange to me that coders would be paid more than system's analysts!