Hi, there--

The problem:
A sample of 320 mobile phone batteries contained 16 defective batteries. How many defective
batteries would you expect to find in a sample of 3000?

A solution:
You can use proportional reasoning to solve this problem. Let x be the number of defective
batteries in the larger sample.

 THere are several different ways to set up a proportion for this problem. Just remember to 
match your units. I like to say the proportion out loud. This keeps me from getting the 
proportion upside down. Here is one possible proportion:

[number of DEFECTIVES in SMALLER sample] over [number of BATTERIES in SMALLER sample] 
equals [number of DEFECTIVES in LARGER sample] over [number of BATTERIES in LARGER 
sample]

Now we substitute in the known values and variable.


Solve for x.
We can cross-multiply here. (NOTE: many teachers frown on the cross-multiply technique. 
If your teacher is one of those, see an alternate method below.)







We would expect to find 150 defective batteries in the larger sample.

SOLUTION METHOD WITHOUT CROSS_MULTIPLYING


Multiply both sides of the equation by 3000 to isolate the variable on the right side.





Simplify left side using multiplication and division.


We have the same answer, 150 defective batteries in the larger sample.

Feel free to email if you have questions about this.

Ms.Figge
math.in.the.vortex@gmail.com