MATHS
posted by BRENDAN
Please show the quickest way to do this question?
Amanda has 20 coins in her purse. She has only 10c,20c and 50c coins, and their total value is $5. If she has more 50c than 10c coins, how many 10c has she?
Thank You

Dean
Are you in algebra using variables 'c'?

BRENDAN
I'm not sure what you mean.

Dean
What grade are you in?

BRENDAN
YEAR 4

Dean
c stands for cents?

BRENDAN
yes c stands for cents.

Dr Russ
I got 4 x 50c = $2
2 x 10c = 20 c
14 x 20c = $2.80c
so she has 2 x 10c 
Reiny
Since you are in year 4, you will be able to solve this algebraically.
let the number of 10c pieces be x
let the number of 20c pieces be y
let the number of 50c pieces be (20xy)
10x + 20y + 50(20xy) = 500
reduces to
4x + 3y = 50
so we need positive integer solutions for x and y
clearly x has to be between 0 and 13
after only two tries, I got
x = 2, and y = 14
then
number of 10c pieces = 2
number of 20c pieces = 14
number of 50c pieces = 20214 = 4
check: 2x10 + 14x20 + 4x50 = 500
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