Mrs Chan has twice as many $5 notes as $10 notes and twice as many $10 notes as $50 notes. She has a total of $1080. How many $10 notes does she have?
number of 50's ---- x
number of 10's ---- 2x
number of 5's ----- 2(2x) = 4x
Now, consider the value of those notes to form your equation.
50x + 10(2x) + 5(4x) = 1080
50x + 20x + 20x = 1080
90x = 1080
x = 12
we defined 10's as 2x
so she has 2(12) or 24 $10 bills
check:
fifties 12
tens 24
fives 48
12(50) + 24(10) + 48(5) = 1080
YUP!!
To find the number of $10 notes Mrs. Chan has, let's start by assigning variables to represent unknown quantities.
Let x be the number of $50 notes Mrs. Chan has.
Since she has twice as many $10 notes as $50 notes, Mrs. Chan has 2x $10 notes.
Similarly, she has twice as many $5 notes as $10 notes, so she has 2 * 2x = 4x $5 notes.
Now, let's calculate the total value of all the notes.
The value of a $50 note is $50 * x = $50x.
The value of a $10 note is $10 * 2x = $20x.
The value of a $5 note is $5 * 4x = $20x.
Since the total value of all her notes is $1080, we can set up the equation:
$50x + $20x + $20x = $1080.
Combining like terms, we get:
$90x = $1080.
To solve for x, divide both sides by $90:
x = $1080 / $90 = 12.
So Mrs. Chan has 12 $50 notes.
She has twice as many $10 notes, which equals 2 * 12 = 24 $10 notes.