System of Equations: Need JUST the equations :)?

Question

Problem 1:
Orange Thirst is 15% orange juice and Quencho is 5% orange juice. how many liters of each should be mixed together in order to get 100 L of a mixture that is 12% orange juice?

Problem 2: A motorboat took 4 hours to make a trip downstream with a 6-mph current. The return trip against the same current took 5 hours. Find the speed of the boat in still water. (Use distance=rate x time)

Thanks. Don't solve it. Just need the equations. :)

Answer 1

For problem 1: If we have x litres of Orange Thirst and y litres of Quencho, we get
x + y = 100
15x + 5y = 1200 (or 0.15x + 0.05y = 12)

For problem 2: If the speed in still water is x mph, the speed with the current is (x+6) mph and the speed against the current is (x-6) mph. Since the distance travelled in both directions is the same, we have
4 (x+6) = 5 (x-6).

Answer 2

Hello

Let o = amt. of Orange added
Let q = amt. of Quen added then

15%0 + 5%q = 12%*100
o + q = 100



Let b= speed of boat in still h20

Then downstream d = (b+6)*4
Then upstream d = (b-6)*5

Now the distance is the same so (b+6)*4 = (b-6)*5 or


Hope This Helps!