Question

It is estimated that 20 patrons will attend an event for every $100 spent in advertising. If tickets cost $40, how much can a promoter expect to increase sales if he spends $10,000 in advertising?

Answer 1

`$80,000`

Explanation:

In working through a word problem like this, read it a few times to understand the scenario being presented, without paying too much attention to the numbers.....Something like....

"If a promoter spends some money on advertising he will attract more patrons."

Summarise the information in short sentences.

The promoter spends $10,000.

"For every $100 spent, 20 patrons are attracted"

"Tickets cost $40"

Now plan the calculations:
(This is our thinking, not necessarily written down)

1) How many $100 payments are there in $10,000?`color(white)(.....)`Divide
2) Each payment brings 20 patrons.`color(white)(............................)`Multiply
3) Each patron buys a $40 ticket.`color(white)(................................)`Multiply

1) `10000/100 = 100" amounts of $100"`

2) `100 xx20 = 2000 " patrons attracted"`

3) `2000 xx 40 = $80,000 " each patron buys a ticket"`

In one calculation this would be:

`(10000xx20xx40)/100`

Answer 2

income is $80,000

Explanation:

Using ratio:`" "("income")/("expenditure")`

`color(blue)("Initial condition:")`

Expenditure `-> $100`
Income `->20xx$40=$800`

So for initial condition we have:

`color(red)(" "("income")/("expenditure") -> 800/100)`

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(blue)("Determine the total income")`

So if $10,000 is spent on advertising (expenditure) we have:

`" "("income")/("expenditure") -> color(red)(800/100)color(green)( -= ("income")/(10,000))`

Multiply both sides by `color(blue)( 10,000)` giving

`color(red)(800/100) color(blue)(xx 10,000) -=color(green)( ("income")/(10,000))color(blue)(xx10,000)`

`(cancel(800)^8xx10,000)/(cancel(100))-="income"xx(cancel(10,000))/(cancel(10,000))`

`"income" = 80,000`