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
Are you in algebra using variables 'c'?
I'm not sure what you mean.
What grade are you in?
YEAR 4
c stands for cents?
yes c stands for cents.
I got 4 x 50c = $2
2 x 10c = 20 c
14 x 20c = $2.80c
so she has 2 x 10c
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 (20-x-y)
10x + 20y + 50(20-x-y) = 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 = 20-2-14 = 4
check: 2x10 + 14x20 + 4x50 = 500
To find the quickest way to solve this question, we can use a systematic approach. First, let's denote the number of 10c coins as "x". Since we know Amanda has more 50c coins than 10c coins, the number of 50c coins must be greater than "x".
Now, we can set up the equation to represent the total value of the coins: 10x + 20(20-x) + 50(20-x) = 500. Let's simplify this equation step by step.
We can start by distributing the numbers inside parentheses:
10x + 400 - 20x + 50(20-x) = 500.
Next, let's distribute the 50 into the second parentheses:
10x + 400 - 20x + 1000 - 50x = 500.
Combine like terms:
-40x + 1400 = 500.
Move 1400 to the other side of the equation:
-40x = 500 - 1400.
Simplify:
-40x = -900.
Divide both sides of the equation by -40:
x = -900 / -40.
Finally, calculate the value of x:
x = 22.5.
Since the number of coins cannot be a fraction, we can conclude that there is no whole number value that satisfies the conditions of the problem. Therefore, Amanda does not have any 10c coins.