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?

25%

Step-by-step explanation:

becouse she is reducing the price

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4