Question

11 Jack and Sadia work for a company that

sells boxes of breakfast cereal. The
company wants to have a special offer.
Here is Jack's idea for the special offer.
Put 25% more cereal into each box and do not change the price.
Here is Sadia's idea.
Reduce the price and do not change the amount of cereal in each
box.
Sadia wants her idea to give the same value for money as Jack's idea.
By what percentage does she need to reduce the price?

Answer 1

20% reduction in price

Explanation:

Let the original price of each box be P and original quantity be Q. The unit rate is P/Q

Jack's approach

increase quantity by 25% = 0.25Q

New quantity = Q + 0.25Q = Q(1 +0.25) = 1.25Q

Unit rate = P/1.25Q

Sadia's approach

Reduce price and keep quantity same

Let price reduction be d% = d/100

Let us denote d/100 as r. This will be a decimal value. For example, a reduction of 10% means that the price is reduced by 0.10

Price reduction = P x r = Pr

New price = P - Pr = P(1-r)

Unit rate by this method =P(1-r) /Q

Both unit rates have to be the same if both values are the same

So

`(P)/(1.25Q) = (P(1-r))/(Q)\\\\(P)/(Q) \cdot (1)/(1.25) = (P)/(Q) \cdot (1-r)\\\\`

Eliminate
`\displaystyle {(P)/(Q)}` common factor from both sides to get

`(1)/(1.25) = 1- r`

`(1)/(1.25) = 0.8\\\\`

So we get

`1 - r = 0.8\\\\\implies r = 1 - 0.8 = 0.2\\\\`

0.2 works out to 0.2 x 100 = 20%

So for Sadia's idea to have the same value as Jack's idea, the price should be reduced by 20%