Question

5e+15p</=60

How many combinations of excersises (e) and problems (p)can you do in exactly one hour(60 minutes)?

I've found 5 combinations:
9e,1p
3e,3p
6e,2p
0e,4p,
12e,0p

Are there anymore? What method would you use to solve this type of problem? Thanks for the help!

Answer 1

graph it
e on x axis
p on y axis

e from 0 to 60/5 = 12
p from 0 to 60/15 = 4

draw line from (0,4) down to (12,0)
everything between the origin and the line in the first quadrant will do, including on the line. Just fill in the grid there.

Answer 2

you have them, e,p are integer solutions

Answer 3

when p = 0, 13 points (0,0)to (12,0)
when p = 1, 10 points (0,1) to (9,1)
when p = 3, 4 points (0,2) to (3,3)
when p = 4, 1 point (0,4)

13 + 10 + 4 + 1 = 28

Answer 4

Oh, sorry, I thought you wanted all integer solutions that satisfied the inequality. The ones you listed are exactly on the line.
I left out p = 2 line
(0, 2) to (6,2), seven more
28 + 7 = 35 total solutions for less than an hour if all are integer.