Coffee
Problem
At a well known store they sell their own blend of coffee. They use:
| Mocha | costing £13 per kilogram |
| Kenyan | costing £14 per kilogram |
| Brazilian | costing £17 per kilogram |
To make 11 kilograms of this blend of coffee costs £15 per kilogram.
This blend uses more Brazilian than Kenyan coffee.
An exact number of kilograms of each type of coffee is used.
How many kilograms of each type of coffee are used?
Student Solutions
Many students used trial and improvement techniques to show that to blend the coffee then 4kg of Mocha, 2 kg of Kenyan and 5 kg of Brazilian are needed if the conditions are to be satisfied. These included students from Maidstone Girls Grammar School; West Flegg Middle School; Madras College; Strabane Grammar School; Trinity Academy, Edinburgh; Our Lady's Grammar School, Newry; Clevedon Community School, Somerset and ACS Barker, Singapore.
Joshua of Russell Lower Scholl, Ampthill, Bedfordshire arrived at his solution which his father called trial and error techniques. There is an easier and quicker way submitted by Lyndsay of Mount school, York, which is represented below:
M + K + B = 11 (11 kg in all)
13M + 14K + 17B = 165 (cost is £165)
so 13 ( 11 - K - B) + 14K + 17B = 165
143 - 13K - 13B + 14K + 17B = 165
K + 4B = 22
Since B > K, the only whole numbers that fit are B = 5 and K
= 2
So the answer is 5 kg Brazilian, 2 kg Kenyan and 4 Kg Mocha.