Carl had a total of 52 notes. The notes are $5 notes and $10 notes. After he spent 80% of the $5 notes and 75% of the $10 notes on one vacuum cleaner, he was left with 2 times as many $10 notes as $5 notes. How much did the vacuum cleaner cost?
|
$5 |
$10 |
Before |
5x1 = 5 u |
4x2 = 8 u
|
Change |
- 4x1 = - 4 u |
- 3x2 = - 6 u
|
After |
1x1 = 1 u |
1x2 = 2 u |
Comparing $5 and $10 in the end |
1x1 = 1 u
|
2x1 = 2 u |
80% of $5 notes =
80
100 of $5 notes =
45 of $5 notes
75% of $10 notes =
75100 of $10 notes =
34 of $10 notes
The number of $5 notes in the end is repeated. Make the number of $5 notes the same. LCM of 1 and 2 is 2.
The number of $10 notes in the end is repeated. Make the number of $10 notes the same. LCM of 1 and 1 is 1.
Number of notes at first
= 5 u + 8 u
= 13 u
13 u = 52
1 u = 52 ÷ 13 = 4
|
$5 |
$10 |
Number |
4 u |
6 u |
Value |
5 |
10 |
Total value |
20 u |
60 u |
Value of $5 spent
= 4 u x 5
= 20 u
Value of $10 spent
= 6 u x 10
= 60 u
Price of the vacuum cleaner
= 20 u + 60 u
= 80 u
= 80 x 4
= $320
Answer(s): $320