Carl had a total of 150 notes. The notes are $5 notes and $10 notes. After he spent 90% of the $5 notes and 75% of the $10 notes on one vacuum cleaner, he was left with 5 times as many $10 notes as $5 notes. How much did the vacuum cleaner cost?
|
$5 |
$10 |
Before |
10x1 = 10 u |
4x5 = 20 u
|
Change |
- 9x1 = - 9 u |
- 3x5 = - 15 u
|
After |
1x1 = 1 u |
1x5 = 5 u |
Comparing $5 and $10 in the end |
1x1 = 1 u
|
5x1 = 5 u |
90% of $5 notes =
90
100 of $5 notes =
910 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 5 is 5.
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
= 10 u + 20 u
= 30 u
30 u = 150
1 u = 150 ÷ 30 = 5
|
$5 |
$10 |
Number |
9 u |
15 u |
Value |
5 |
10 |
Total value |
45 u |
150 u |
Value of $5 spent
= 9 u x 5
= 45 u
Value of $10 spent
= 15 u x 10
= 150 u
Price of the vacuum cleaner
= 45 u + 150 u
= 195 u
= 195 x 5
= $975
Answer(s): $975