Answer:
- ratio -- bean : tomato = 3 : 5
- bean height -- 30 cm
- tomato height -- 50 cm
Step-by-step explanation:
The problem statement tells you the ratio of heights is ...
(bean height) = (3/5)×(tomato height)
Dividing this expression by the height of the tomato plant gives ...
(bean height)/(tomato height) = 3/5
which can also be expressed as ...
(bean height) : (tomato height) = 3 : 5
__
The 3 "ratio units" of bean plant height differ from the 5 "ratio units" of tomato plant height by 2 "ratio units". The actual difference is 20 cm, so each of those 2 "ratio units" corresponds to (20 cm)/2 = 10 cm. Then the height ratio can be multiplied by this value to find the individual plant ratios:
(bean height) : (tomato height) = 30 cm : 50 cm
- The height of the bean plant is 30 cm.
- The height of the tomato plant is 50 cm.
_____
Alternate solution
When we subtract the bean plant height from the tomato plant height, we get ...
height difference = (tomato height) - (bean height)
= (tomato height) - (3/5)(tomato height) = (2/5)(tomato height)
Since the height difference is 20 cm, we have ...
(2/5)(tomato height) = 20 cm
tomato height = 50 cm . . . . . . . . . multiply by 5/2
bean height = (3/5)(50 cm) = 30 cm
