Carl had a total of 70 notes. The notes are $10 notes and $5 notes. After he spent 90% of the $10 notes and 60% of the $5 notes on one speaker, he was left with 3 times as many $5 notes as $10 notes. How much did the speaker cost?
|
$10 |
$5 |
Before |
10x2 = 20 u |
5x3 = 15 u
|
Change |
- 9x2 = - 18 u |
- 3x3 = - 9 u
|
After |
1x2 = 2 u |
2x3 = 6 u |
Comparing $10 and $5 in the end |
1x2 = 2 u
|
3x2 = 6 u |
90% of $10 notes =
90
100 of $10 notes =
910 of $10 notes
60% of $5 notes =
60100 of $5 notes =
35 of $5 notes
The number of $10 notes in the end is repeated. Make the number of $10 notes the same. LCM of 2 and 3 is 6.
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.
Number of notes at first
= 20 u + 15 u
= 35 u
35 u = 70
1 u = 70 ÷ 35 = 2
|
$10 |
$5 |
Number |
18 u |
9 u |
Value |
10 |
5 |
Total value |
180 u |
45 u |
Value of $10 spent
= 18 u x 10
= 180 u
Value of $5 spent
= 9 u x 5
= 45 u
Price of the speaker
= 180 u + 45 u
= 225 u
= 225 x 2
= $450
Answer(s): $450