Help please?

Question

Maggie has a job working in an office for $10 an hour and another job driving a tractor for $12 an hour. One week she works in the office twice as long as she drives the tractor. Her total income for that week is $416. How many hours did she spend at each job?

Answer 1

Hello, thank you for taking the time to post your question!

If you let “t” represent the number of hours that Maggie drove the tractor, then the equation for the weekly wages here is

12t + 10(2t) = 416   because she made $416 total and she worked twice as long in the office

From there then you can solve that expression algebraically for the value of “t”

12t + 20t = 416

32t = 416

t = 416/32 = 13, meaning that Maggie worked 13 hours driving the tractor

then for the office hours you want to take 2(13) = 26, meaning that she spent 26 hours working in the office

I hope that helps you get moving in a better direction on this type of question! Feel free to reach out if you have any additional questions beyond that :)

Answer 2

set up 10x+12y that is your sum of monies. skip over see 416 dollars total in a week. 10x + 12y = 416 and note that x doubles y because she works in the office twice as long as she drives the tractor. thus your equation is y = 1/2x

 

we get an equation and need to interpolate so that 10x >> 12 1/2 x. Solve 10x +12(1/2x) = 416 = 16x=416 so that x=26.

 

The solution is that the first job spent 10 times 16 equal to 160. the second job is the subtration of 416 and 160, thats the tractor job.