SOLUTION: A week ago, Sandy�s seasonal Little League batting average was 360. After five more at bats this week, Sandy�s batting average is up to 400. What is the smallest number of hits tha

Question 293200: A week ago, Sandy�s seasonal Little League batting average was 360. After five more at bats this week, Sandy�s batting average is up to 400. What is the smallest number of hits that Sandy could have had this season?
Found 2 solutions by josmiceli, richwmiller:
Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
The batting average is (hits)/(number of times at bat) x 1000
Let = times at bat last week
Let = number of hits last week
Let = number of hits this week
(1)
and after this week:
(2)
------------------------------
This is 2 equations and 3 unknowns, so it isn't
directly solvable, but it can be analyzed
From (1):
(1)

and from (2)

I know that
Suppose
ends up being (-), so that doesn't work
Suppose . Then , and that can't be
Suppose

From (1)

and from (2):
(2)
(2)
The smallest number of hits Sandy could have got this
season is , or 12 hits

OK

Answer by richwmiller(17219) (Show Source): You can put this solution on YOUR website!
x/y=.36,
(x+z)/(y+5)=.4,
z<=5
9 before the last five at bats
12 after the last five
9/25 3 of the last five
9/25=.36
12/30=2/5=.4
18/50 4 of the last 5
18/50=.36
22/55=2/5=.4
27/75 5 of the last 5
27/75=.36
32/80=4/10=2/5=.4

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