Small grapefruits |
Medium grapefruits |
Large grapefruits |
$4 |
$5 |
$6 |
Harry had some grapefruits in 3 sizes. The number of medium grapefruits was twice 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 $216 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 |
|
2x3 |
1x3 |
1x1 |
|
3x1 |
1 u |
6 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 |
6 u |
3 u |
Change |
- 1 u |
- 6 u |
- 2 u |
After |
0 |
0 |
1 u |
Number of large grapefruits that Harry sold
=
23 x 3 u
= 2 u
|
Small grapefruits |
Medium grapefruits |
Large grapefruits |
Number |
1 u |
6 u |
2 u |
Value |
$4 |
$5 |
$6 |
Total value |
4 u |
30 u |
12 u |
Amount that Harry received from selling of
23 of the large grapefruits = 12 u
12 u = 216
1 u = 216 ÷ 12 = 18
Number of large grapefruits at first
= 3 u
= 3 x 18
= 54
(b)
Amount that Harry collected less from selling the small grapefruits than the medium grapefruits
= 30 u - 4 u
= 26 u
= 26 x 18
= $468
Answer(s): (a) 54; (b) $468