SOLUTION: Please help - its my daughters math and I can not figure this out to help her!! Thanks! Sergio walked to and from school on 3/5 of the days in one month. He got a ride to school

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: Please help - its my daughters math and I can not figure this out to help her!! Thanks! Sergio walked to and from school on 3/5 of the days in one month. He got a ride to school      Log On


   

Question 946624: Please help - its my daughters math and I can not figure this out to help her!! Thanks!
Sergio walked to and from school on 3/5 of the days in one month. He got a ride to school on ⅞ of remaining days. On the one remaining day he stayed home with a cold. How many school days were there that month?
Found 2 solutions by Alan3354, josgarithmetic:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Sergio walked to and from school on 3/5 of the days in one month. He got a ride to school on 7/8 of remaining days. On the one remaining day he stayed home with a cold. How many school days were there that month?
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d = # of school days
---
(3/5)d + (7/8)(d - (3/5)d) + 1 = d
3d/5 + (7/8)*(2d/5) + 1 = 3d/5 + 7d/20 + 1 = d
Multiply by 20 to eliminate fractions
12d + 7d + 20 = 20d
19d + 20 = 20d
d = 20
--> 20 days

Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
Such common fractions as 3%2F5 and 7%2F8 suggest that the month should be a nonprime value like 30.

m, how many days in the month used.

(this part is poorly stated, but I leave it here anyway)----%282%2F5%29m is for the 7%2F8of m remaining before the 1 day left still remaining.-----


-----(this part makes good sense)-------
highlight_green%28%282%2F5%29m-%287%2F8%29%28%282%2F5%29m%29=1%29, which required a thought process not easily expressed as steps in the mind. Try to think what it says as shown, and when understood, solve for m.

%282%2F5%29m-%287%2F%284%2A5%29%29m=1
8m-7m=20
highlight%28m=20%29

This was very likely February which usually has 28 days, and if school is only 5 days per week, then the m=20 accounts as four weeks, therefore most likely February.