Carl had a total of 40 notes. The notes are $10 notes and $2 notes. After he spent 90% of the $10 notes and 60% of the $2 notes on one vacuum cleaner, he was left with 4 times as many $2 notes as $10 notes. How much did the vacuum cleaner cost?

	$10	$2
Before	10x1 = 10 u	5x2 = 10 u
Change	- 9x1 = - 9 u	- 3x2 = - 6 u
After	1x1 = 1 u	2x2 = 4 u
Comparing $10 and $2 in the end	1x1  = 1 u	4x1 = 4 u

90% of $10 notes = ⁹⁰
₁₀₀ of $10 notes = ⁹₁₀ of $10 notes
60% of $2 notes = ⁶⁰₁₀₀ of $2 notes = ³₅ of $2 notes

The number of $10 notes in the end is repeated.  Make the number of $10 notes the same.  LCM of 2 and 4 is 4.

The number of $2 notes in the end is repeated. Make the number of $2 notes the same. LCM of 1 and 1 is 1.

Number of notes at first
= 10 u + 10 u
= 20 u

20 u = 40

1 u = 40 ÷ 20 = 2

	$10	$2
Number	9 u	6 u
Value	10	2
Total value	90 u	12 u

Value of $10 spent
= 9 u x 10
= 90 u

Value of $2 spent
= 6 u x 2
= 12 u

Price of the vacuum cleaner
= 90 u + 12 u
= 102 u
= 102 x 2
= $204

Answer(s): $204