Elimination Method

A question sent in by Jared

Mrs Goh had a sum of money. If she bought 32 apples and 9 pears, she would have $10.40 left. If she bought 12 apples and 24 pears, she would have $14.40 left. Given that she had $30, how many apples could she buy?

Solution:

'Buy two get one free' Question

Question:

Mr Lee bought some files at $4 each and sold them at $10 each. The customers who bought 2 files from him were given 1 file for free. Yesterday, all his customers bought either one or two files. At the end of the day, he had given away 120 files and had earned $1230. Find the number of customers who bought only one file. 

Solution:

'Set' Question

Question: 



Solution:

It can be solved using 'set'

1 set --> 8 bags of sweets and 1 bag of chocolate
Money collected for 1 set --> 8 x 5.5 + 2 = 46
No. of sets = 3128 / 46 = 68

No. of sweets sold --> 68 x 8 x 4 = 2176
No. of chocolates sold --> 68 x 8 = 544

Number of Coins

Another question today.

Adam has 46 10-cent, 20-cent and 50-cent coins which add up to $14.60. There were 9 10-cent coins and the rest were 20-cent coins and 50-cent coins. How many 20-cent and 50-cent coins were there?

Solution:

10-cent coins --> $0.90
so 37 coins (20-cent coins + 50-cent coins) --> $14.60 - $0.90 = $13.70

Here we use assumption method to find the answer:

Assume all 37 coins are 50-cent coin --> 37 x $0.50 = $18.50
Difference --> $18.50 - $13.70 = $4.80
Exchange --> $0.50 - $0.20 = $0.30 
Number of 20-cent coin --> $4.80 ÷ $0.30 = 16
Number of 50-cent coin --> 37 - 16 = 21