Question

Jill's mother limited her XBOX 1 playing to 10 hours per week. She played on only four days, a different amount of time each day. On Saturday, she played twice as much as on Wednesday.she didn't play on Monday, Tuesday, or Thursday. On Friday , she played the least of the days she played.if the times were all different and there were not any partial hours, how many hours did she play on each day?

Answer 1

Hello!

Let's put this down into someone of an equation. On the top of our heads we know she didn't play on Monday, Tuesday, or Thursday. This means she played on Wednesday, Friday, Saturday, and Sunday. We will use the variables w, f, s, and o, with o representing Sunday. .

s=2w
f<s
f<w
f<o
w+f+s+o=10

Since we already know what s equals, we also know that w is 1/2 of the time played on Saturday. Let's try to substitute s into the last equation to see if we can find anything.

w+f+2w+o=10
3w+f+o=10

Now we just need to worry about Friday and Sunday. We know that Friday was played the least. Let's try substituting 2w for s in one the equations.

f<2w

This means that f cannot be 2w. But it also cannot be w either, since all of the times were different. It has to be less than w. Perhaps we could try using 0.5w in our equation and see if it would all add up to 10

3.5w+o=10

Given that there are no partial hours, w has to equal 2, because if we did 1, then o would be partial, and if we did 3 it would be more than ten. Now that we have the value of w we can find all of the numbers.

s=2(2)
s=4

Now we have four hours left. We can only split this up in one way, 3 and 1, since 2 and 2 are the same and all of the times are different. Since we know Friday is the least, we know that f=1, and that leaves o=3.

Wednesday: 2 hours
Friday: 1 hour
Saturday: 4 hours
Sunday :3 hours

I hope this helps!