If Jim earns x dollars per hour, it will take him 4 hours to

[ms100]

If Jim earns x dollars per hour, it will take him 4 hours to earn exactly enough money to purchase a particular jacket. If Tom earns y dollars per hour, it will take him exactly 5 hours to earn enough money to purchase the same jacket. How much does the jacket cost?

(1) Tom makes 20% less per hour than Jim does.

(2) x + y = $43.75

Ok, I need some help with my rate problems, please help me understand statement 2.

Thanks,
Mariela

[StaceyKoprince]

No problem. FYI, if you are in our course, don't forget to use your free half hour of weekly tutoring - but you have to use it every week because it expires!

x and y represent, respectively, Jim's hourly rate and Tom's hourly rate. So x+y represents how much they earn (collectively) in 1 hour. 4x represents what Jim would have to earn (by working 4 hours) to buy one shirt and 5y represents what Tom would have to earn (by working 5 hours) to buy one shirt.

Given the information in the question, we know something about the relationship between x and y. If Jim works 4 hours at x dollars per hour, he'll earn the same amount as Tom does when Tom works 5 hours at y dollars per hour. So 4x = 5y.

I now have two equations and two variables, which is usually sufficient, but I'm going to check a little more just in case, because this is data sufficiency after all. :)

4x = 5y
x+y = 43.75

I can rearrange the first equation to: x = 5y/4 and substitute into the second:
(5y/4) + y = 43.75 then multiply each term by 4
5y + 4y = 4(43.75) note that I don't multiply out the 4 on the right. I'll only multiply at the end (if I have to)
9y = 4(43.75)
y = [4(43.75)] / 9
This will let me get one number for y (not that I'm actually going to calculate it!). If I can find a value for y, then I can find a value for 5y, which is how much the jacket costs. Sufficient.