Carl had a total of 100 notes. The notes are $10 notes and $5 notes. After he spent 90% of the $10 notes and 80% of the $5 notes on one television set, he was left with 2 times as many $5 notes as $10 notes. How much did the television set cost?
|
$10 |
$5 |
Before |
10x1 = 10 u |
5x2 = 10 u
|
Change |
- 9x1 = - 9 u |
- 4x2 = - 8 u
|
After |
1x1 = 1 u |
1x2 = 2 u |
Comparing $10 and $5 in the end |
1x1 = 1 u
|
2x1 = 2 u |
90% of $10 notes =
90
100 of $10 notes =
910 of $10 notes
80% of $5 notes =
80100 of $5 notes =
45 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 2 is 2.
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 + 10 u
= 20 u
20 u = 100
1 u = 100 ÷ 20 = 5
|
$10 |
$5 |
Number |
9 u |
8 u |
Value |
10 |
5 |
Total value |
90 u |
40 u |
Value of $10 spent
= 9 u x 10
= 90 u
Value of $5 spent
= 8 u x 5
= 40 u
Price of the television set
= 90 u + 40 u
= 130 u
= 130 x 5
= $650
Answer(s): $650