Question

A cereal company’s research indicates that their advertising and sales of a new brand of cereal follow a linear relationship.

If it spends €500,000 on advertising, 120,000 boxes of cereal will be sold and if it spends €620,000, then 150,000 boxes will be sold.

Determine how much advertising must be spent to sell 250,000 boxes of cereal

Answer 1

SOLUTION

GIVEN

A cereal company’s research indicates that their advertising and sales of a new brand of cereal follow a linear relationship.

If it spends €500,000 on advertising, 120,000 boxes of cereal will be sold and if it spends €620,000, then 150,000 boxes will be sold.

TO DETERMINE

The amount for advertising must be spent to sell 250,000 boxes of cereal

EVALUATION

Let € x must be spent to sell n boxes of cereal

Now it is given that if it spends €500,000 on advertising, 120,000 boxes of cereal will be sold and if it spends €620,000, then 150,000 boxes will be sold

So there are two points ( 120000, 500000) & ( 150000, 620000)

Thus linear equation is

$\displaystyle \sf{ \frac{x - 500000}{n - 120000} = \frac{620000 - 500000}{150000 - 120000} }$

$\displaystyle \sf{ \implies \: \frac{x - 500000}{n - 120000} = \frac{120000 }{30000} }$

$\displaystyle \sf{ \implies \: \frac{x - 500000}{n - 120000} = 4 }$

$\displaystyle \sf{ \implies \: x - 500000 = 4 (n - 120000)}$

$\displaystyle \sf{ \implies \: x - 500000 = 4 n - 480000)}$

$\displaystyle \sf{ \implies \: x = 4 n + 20000}$

Hence the required relationship is

$\boxed{ \: \displaystyle \sf{ \: x = 4 n + 20000} \: \: }$

Now we have to find the amount for advertising must be spent to sell 250,000 boxes of cereal

So n = 250000

We get

$\displaystyle \sf{ x = 4 \times 250000 + 20000}$

$\displaystyle \sf{ \implies \: x = 1000000 + 20000}$

$\displaystyle \sf{ \implies \: x = 1020000 }$

FINAL ANSWER

The amount for advertising must be spent to sell 250,000 boxes of cereal = € 1020000

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