## Friday, December 25, 2015

### [S1_20151225ABEX] Apples and Cherries on Christmas?

Problem

 The ratio of the mass of an apple to the mass of two cherries is  9 : 1.  The mass of the apple is  150 g.  What is the number of cherries that can be found in  y  kg?

Solution

Remarks
To obtain the answer, we made a simplifying assumption that all the apples and cherries are identical in mass.  The answer is an algebraic expression and it can be obtained by following the same procedure one would solve the problem if it were in concrete numbers.  Learning algebra is like learning a new but more powerful language.  It takes some time getting used to.  Since we do not know the value of  y,  we leave the answer in terms of  y.  But if we knew the value of  y,  we would know that the answer is  120 times that.  For example, with  3 kg,  we get (about)  360 cherries.

H02. Use a diagram / model
H05. Work backwards
H08. Make suppositions
H10. Simplify the problem
H11. Solve part of the problem

Suitable Levels
Primary 6 Mathematics (challenge)
Lower Secondary Mathematics (Secondary 1)
GCE ‘O’ Level “Elementary” Mathematics (revision)
* other syllabuses that involve ratios and algebra