Question

Hector Villanueva has a 0.300 batting average (hits/times at bat). If he gets a total of 10 more hits the next 10 times at bat, his batting average will jump to 0.400. Determine how many hits he had originally.

Answer 1

@jim_thompson5910

Answer 2

Let x = number of hits originally and y = number of at bats originally

Answer 3

Based on those definitions, we know that the batting average currently is x/y

but that's also equal to 0.300 or just 0.3

Answer 4

So x/y = 0.3

Solve for x to get x = 0.3y

Answer 5

Now add 10 to each stat to get x+10 hits over y+10 at bats

The new batting average is (x+10)/(y+10) and this is given to be 0.4

So,

(x+10)/(y+10) = 0.4

Answer 6

How did you get 0.3y?

Answer 7

x/y = 0.3

x = 0.3y ... multiply both sides by y to isolate x

Answer 8

Once you have (x+10)/(y+10) = 0.4, you can plug in x = 0.3y to get

(x+10)/(y+10) = 0.4

(0.3y+10)/(y+10) = 0.4

now you have an equation with just y in it. So you can solve for y.

After finding the value of y, you can use it to find the value of x

Answer 9

Sorry I am just in middle school so I don't really get how to do this stuff. Can you help me through this in. Str

Answer 10

*Step by step way?

Answer 11

@jim_thompson5910

Answer 12

Do you see how I got (0.3y+10)/(y+10) = 0.4