Question 636339
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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.
{{{16/320=x/3000}}}

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.)

{{{(16)(3000)=320x}}}

{{{x=((16)(3000))/320}}}

{{{x=150}}}

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

SOLUTION METHOD WITHOUT CROSS_MULTIPLYING
{{{16/320=x/3000}}}

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

{{{3000*(16/320)=3000*(x/3000)}}}

{{{((3000*16)/320)=x}}}

Simplify left side using multiplication and division.
{{{x=150}}}

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
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