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

Algebra ->  Average -> 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      Log On


   

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) About Me  (Show Source):
You can put this solution on YOUR website!
The batting average is (hits)/(number of times at bat) x 1000
Let x = times at bat last week
Let h = number of hits last week
Let n = number of hits this week
(1) 360%2F1000+=+h%2Fx
and after this week:
(2) 400%2F1000+=+%28h+%2B+n%29%2F%28x+%2B+5%29
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This is 2 equations and 3 unknowns, so it isn't
directly solvable, but it can be analyzed
From (1):
(1) 360%2F1000+=+h%2Fx
.36+=+h%2Fx
x+=+h%2F.36
x+=+2.778h
and from (2)
.4+=+%28h+%2B+n%29%2F2.778h+%2B+5%29
.4%2A%282.778h+%2B+5%29+=+h+%2B+n
1.111h+%2B+2+=+h+%2B+n
.111h+%2B+2+=+n
I know that n+%3C=+5
Suppose n+=+1
h ends up being (-), so that doesn't work
Suppose n+=+2. Then h+=+0, and that can't be
Suppose n+=+3
.111h+=+1
h+=+9
From (1)
.36+=+h%2Fx
x+=+9%2F.36
x+=+25
and from (2):
(2) 400%2F1000+=+%28h+%2B+n%29%2F%28x+%2B+5%29
(2) .4+=+%289+%2B+3%29%2F%2825+%2B+5%29
The smallest number of hits Sandy could have got this
season is h+%2B+n, or 12 hits
.4+=+12%2F30
12+=+12
OK







Answer by richwmiller(17219) About Me  (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