Question

The United States Department of Agriculture reports that 16% of Americans are now on food stamps. If there are 310,000,000 Americans, how many are on food stamps?

Answer 1

See the explanation

Explanation:

Total Americans = 310,000,000

Americans on food stamps

`" = 16 % of 310,000,000"`

`= 16/100 times 310,000,000`

`= 16/cancel100 times (3100000cancel00)`

`= 16 times 3100000`

`" = 49,600,000 Americans"`

Answer 2

`49600000` people

Explanation:

Remember that percentage is out of a hundred. So, we can rewrite `16%` as `16/100`.

Then we multiply this with `310000000`.

`16/100*310000000`

`=49600000` people are on food stamps

Answer 3

Answered as if this was a non calculator question

`49,600,000`

Explanation:

Percentage is basically a fraction. However, it is a special fraction in that the bottom number (denominator) is ALWAYS fixed at 100.

There are two ways of writing percentage and they both represent exactly the same thing.

So one way for sixteen percent is `16%` and the other way is `16/100`

In one sense we have the following comparison:

`16%->16xx%`
`16/100color(white)(".")->16xx1/100`

So by direct comparison the % in `16%` is the same as `xx1/100`

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

When converting words in a question the use of 'of' is translated as multiply. So we have:

`ubrace(color(white)("d")16% color(white)("dd.dd"))color(white)("dd")" of "color(white)("ddd")310,000,000`
`color(white)("ddddddddddddd")darr`
`obrace(16xx1/100color(white)("dd")) color(white)("..dd")xxcolor(white)("dddd")310,000,000`

cancel out the 100

`16/(cancel(100))xx310,000,0cancel(00)`

`16xx3,100,000`

This is the same as `16xx31xx10^5`

Ignoring the `10^5` for now.

`color(white)("d")16`
`ul(color(white)("d")31)`
`480larr 30xx16`
`ul(color(white)("d")16 larr 1 xx16)`
`496larr" Added"`

Putting it together we have:

`496xx10^5 = 49,600,000`

or in scientific notation: `4.96 xx 10^7`