Ted practices two types of swimming styles for a total of 50 minutes every day. he spends 20 minutes more practicing the breast stroke than the butterfly stroke.
part a: write a pair of linear equations to show the relationship between the number of minutes ted practices the butterfly stroke every day (x) and the number of minutes he practices the breast stroke every day (y). (5 points)
part b: how much time does ted spend on practicing the breast stroke every day? (3 points)
part c: is it possible for ted to have spent 45 minutes practicing the butterfly stroke every day? explain your reasoning. (2 points)

So we know that he spends 20 more minutes on breast stroke and 50 mins total. then we can create this system of equations:
x + y = 50
y = x + 20

now that we have our system of equations, we can solve them. we'll start by substituting 2 into 1:
x + (x + 20) = 50
2x + 20 = 50
x + 10 = 25
x = 25 - 10 = 15
substitute our new x into the second equation:
y = 15 + 20 = 35
so he spends 35 minutes on breaststroke.

it's not possible for ted to have spent 45 minutes on butterfly because it told us that he spent 50 minutes total and more time on breaststroke than butterfly. if he spent 45 minutes on butterfly then he only spent 5 mins on breaststroke, and that's not more than 45 so it's impossible.

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