Carl had a total of 180 notes. The notes are $2 notes and $5 notes. After he spent 90% of the $2 notes and 80% of the $5 notes on one television set, he was left with 2 times as many $5 notes as $2 notes. How much did the television set cost?
|
$2 |
$5 |
Before |
10x1 = 10 u |
5x2 = 10 u
|
Change |
- 9x1 = - 9 u |
- 4x2 = - 8 u
|
After |
1x1 = 1 u |
1x2 = 2 u |
Comparing $2 and $5 in the end |
1x1 = 1 u
|
2x1 = 2 u |
90% of $2 notes =
90
100 of $2 notes =
910 of $2 notes
80% of $5 notes =
80100 of $5 notes =
45 of $5 notes
The number of $2 notes in the end is repeated. Make the number of $2 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 = 180
1 u = 180 ÷ 20 = 9
|
$2 |
$5 |
Number |
9 u |
8 u |
Value |
2 |
5 |
Total value |
18 u |
40 u |
Value of $2 spent
= 9 u x 2
= 18 u
Value of $5 spent
= 8 u x 5
= 40 u
Price of the television set
= 18 u + 40 u
= 58 u
= 58 x 9
= $522
Answer(s): $522