Tim and Jane both work for a company that sells boxes of breakfast cereal. The boxes of cereal cost £3.00 and the amount of cereal in each box weighs 160g. The company wants to have a special offer 25% more cereal in each box do not change the price Here is Janes idea reduce the price and do not change the amount of cereal added in the box jane wants her idea to give the same value for money as tims idea. By what percentage does she need to reduce the price

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MrRoyal MrRoyal · Answer 1 · 2021-05-26T04:38:29+02:00

Answer:

20% reduction

Step-by-step explanation:

Given

[tex]Price = 3.00[/tex]

[tex]Weight = 160g[/tex]

[tex]Rate = 25\%[/tex]

Required

Price reduction in Jane's idea

First, calculate the new weight of the box (the original plan)

[tex]New = Weight * (1 + Rate)[/tex]

[tex]New = 160g * (1 + 25\%)[/tex]

Express 1 as percentage

[tex]New = 160g * (100\% + 25\%)[/tex]

[tex]New = 160g * (125\%)[/tex]

[tex]New = 200g[/tex]

So, the original idea is:

[tex]200g \to #3.00[/tex]

i.e. 200g costs 3 pounds each

Calculate unit price

[tex]Unit = \frac{3.00}{200}[/tex]

[tex]Unit = 0.015[/tex] pound per gram

For Jane's idea, the price of each box will be:

[tex]Price = Weight *Unit[/tex]

[tex]Price = 160 * 0.015[/tex]

[tex]Price = 2.40[/tex] pound

The percentage reduction is then calculated as:

[tex]\% Reduction = \frac{Original\ Price -Janes\ Price}{Original\ Price} * 100\%[/tex]

[tex]\% Reduction = \frac{3.00 - 2.40}{3.00} * 100\%[/tex]

[tex]\% Reduction = \frac{0.6}{3.00} * 100\%[/tex]

[tex]\% Reduction = \frac{60}{3.00}\%[/tex]

[tex]\% Reduction = 20\%[/tex]