Carl had a total of 40 notes. The notes are $5 notes and $2 notes. After he spent 90% of the $5 notes and 80% of the $2 notes on one lamp, he was left with 2 times as many $2 notes as $5 notes. How much did the lamp cost?
|
$5 |
$2 |
Before |
10x1 = 10 u |
5x2 = 10 u
|
Change |
- 9x1 = - 9 u |
- 4x2 = - 8 u
|
After |
1x1 = 1 u |
1x2 = 2 u |
Comparing $5 and $2 in the end |
1x1 = 1 u
|
2x1 = 2 u |
90% of $5 notes =
90
100 of $5 notes =
910 of $5 notes
80% of $2 notes =
80100 of $2 notes =
45 of $2 notes
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.
The number of $2 notes in the end is repeated. Make the number of $2 notes the same. LCM of 1 and 1 is 1.
Number of notes at first
= 10 u + 10 u
= 20 u
20 u = 40
1 u = 40 ÷ 20 = 2
|
$5 |
$2 |
Number |
9 u |
8 u |
Value |
5 |
2 |
Total value |
45 u |
16 u |
Value of $5 spent
= 9 u x 5
= 45 u
Value of $2 spent
= 8 u x 2
= 16 u
Price of the lamp
= 45 u + 16 u
= 61 u
= 61 x 2
= $122
Answer(s): $122