Carl had a total of 180 notes. The notes are $2 notes and $5 notes. After he spent 90% of the $2 notes and 60% of the $5 notes on one television set, he was left with 5 times as many $5 notes as $2 notes. How much did the television set cost?
|
$2 |
$5 |
Before |
10x2 = 20 u |
5x5 = 25 u
|
Change |
- 9x2 = - 18 u |
- 3x5 = - 15 u
|
After |
1x2 = 2 u |
2x5 = 10 u |
Comparing $2 and $5 in the end |
1x2 = 2 u
|
5x2 = 10 u |
90% of $2 notes =
90
100 of $2 notes =
910 of $2 notes
60% of $5 notes =
60100 of $5 notes =
35 of $5 notes
The number of $2 notes in the end is repeated. Make the number of $2 notes the same. LCM of 2 and 5 is 10.
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 + 25 u
= 45 u
45 u = 180
1 u = 180 ÷ 45 = 4
|
$2 |
$5 |
Number |
18 u |
15 u |
Value |
2 |
5 |
Total value |
36 u |
75 u |
Value of $2 spent
= 18 u x 2
= 36 u
Value of $5 spent
= 15 u x 5
= 75 u
Price of the television set
= 36 u + 75 u
= 111 u
= 111 x 4
= $444
Answer(s): $444