Small grapefruits |
Medium grapefruits |
Large grapefruits |
$4 |
$5 |
$9 |
Lee had some grapefruits in 3 sizes. The number of medium grapefruits was four times the number of large grapefruits. The number of large grapefruits were thrice the number of small grapefruits. He sold all the small and medium grapefruits. He received $198 from selling
23 of the large grapefruits.
- How many large grapefruits did he have at first?
- How much less did he collect from selling the small grapefruits than the medium grapefruits?
Small grapefruits |
Medium grapefruits |
Large grapefruits |
|
4x3 |
1x3 |
1x1 |
|
3x1 |
1 u |
12 u |
3 u |
(a)
The number of large grapefruits is the repeated identity. Make the number of large grapefruits the same. LCM of 1 and 3 is 3.
|
Small grapefruits |
Medium grapefruits |
Large grapefruits |
Before |
1 u |
12 u |
3 u |
Change |
- 1 u |
- 12 u |
- 2 u |
After |
0 |
0 |
1 u |
Number of large grapefruits that Lee sold
=
23 x 3 u
= 2 u
|
Small grapefruits |
Medium grapefruits |
Large grapefruits |
Number |
1 u |
12 u |
2 u |
Value |
$4 |
$5 |
$9 |
Total value |
4 u |
60 u |
18 u |
Amount that Lee received from selling of
23 of the large grapefruits = 18 u
18 u = 198
1 u = 198 ÷ 18 = 11
Number of large grapefruits at first
= 3 u
= 3 x 11
= 33
(b)
Amount that Lee collected less from selling the small grapefruits than the medium grapefruits
= 60 u - 4 u
= 56 u
= 56 x 11
= $616
Answer(s): (a) 33; (b) $616