Applications of Linear Systems (with ratios)?

Question

Can you show me how to do these? For the first two I have to write a system of two equations.

Kay spends 250 minutes/week exercising. Her ratio of time spent on aerobics to time spent on weight training is 3 to 2. How many minutes per week does she spend on each exercise? Let a = the amount of time spent on aerobics each week, and w = the amount of time spent on weight training each week.

--I know the first equation is 250=a+w. How do I write the other one?

A new parking lot has spaces for 450 cars. The ratio of space for large cars to small cars is 11 to 4. How many spaces are for large cars, how many are for small cars? Let L = the number of spaces for large cars, and S = the number of spaces for small cars.

--The first equation is 450 = L + S. How do I do the second equation?

Answer 1

1)

250 = a+w

3/2 = a/w =>3w=2a

Substituting gives

=>500=5w

=>w=100

=>a=150

2)

450 = L+S

11/4 = L/S =>11S=4L

Substituting gives

1800=15S

=>S=120

=>L=330