Small grapefruits |
Medium grapefruits |
Large grapefruits |
$4 |
$5 |
$8 |
Liam had some grapefruits in 3 sizes. The number of medium grapefruits was twice the number of large grapefruits. The number of large grapefruits were five times the number of small grapefruits. He sold all the small and medium grapefruits. He received $112 from selling
25 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 |
|
2x5 |
1x5 |
1x1 |
|
5x1 |
1 u |
10 u |
5 u |
(a)
The number of large grapefruits is the repeated identity. Make the number of large grapefruits the same. LCM of 1 and 5 is 5.
|
Small grapefruits |
Medium grapefruits |
Large grapefruits |
Before |
1 u |
10 u |
5 u |
Change |
- 1 u |
- 10 u |
- 2 u |
After |
0 |
0 |
3 u |
Number of large grapefruits that Liam sold
=
25 x 5 u
= 2 u
|
Small grapefruits |
Medium grapefruits |
Large grapefruits |
Number |
1 u |
10 u |
2 u |
Value |
$4 |
$5 |
$8 |
Total value |
4 u |
50 u |
16 u |
Amount that Liam received from selling of
25 of the large grapefruits = 16 u
16 u = 112
1 u = 112 ÷ 16 = 7
Number of large grapefruits at first
= 5 u
= 5 x 7
= 35
(b)
Amount that Liam collected less from selling the small grapefruits than the medium grapefruits
= 50 u - 4 u
= 46 u
= 46 x 7
= $322
Answer(s): (a) 35; (b) $322