Carl had a total of 44 notes. The notes are $10 notes and $5 notes. After he spent 90% of the $10 notes and 75% of the $5 notes on one vacuum cleaner, he was left with 3 times as many $5 notes as $10 notes. How much did the vacuum cleaner cost?
|
$10 |
$5 |
Before |
10x1 = 10 u |
4x3 = 12 u
|
Change |
- 9x1 = - 9 u |
- 3x3 = - 9 u
|
After |
1x1 = 1 u |
1x3 = 3 u |
Comparing $10 and $5 in the end |
1x1 = 1 u
|
3x1 = 3 u |
90% of $10 notes =
90
100 of $10 notes =
910 of $10 notes
75% of $5 notes =
75100 of $5 notes =
34 of $5 notes
The number of $10 notes in the end is repeated. Make the number of $10 notes the same. LCM of 1 and 3 is 3.
The number of $5 notes in the end is repeated. Make the number of $5 notes the same. LCM of 1 and 1 is 1.
Number of notes at first
= 10 u + 12 u
= 22 u
22 u = 44
1 u = 44 ÷ 22 = 2
|
$10 |
$5 |
Number |
9 u |
9 u |
Value |
10 |
5 |
Total value |
90 u |
45 u |
Value of $10 spent
= 9 u x 10
= 90 u
Value of $5 spent
= 9 u x 5
= 45 u
Price of the vacuum cleaner
= 90 u + 45 u
= 135 u
= 135 x 2
= $270
Answer(s): $270