a bean plant is 3/5 as tall as a tomato plant. the tomato plant is 20 cm taller than the bean plant. what is the ratio of the bean plant height to the tomato plant height?how tall is the bean plant? the tomato plant ?
Accepted Solution
A:
Answer:ratio -- bean : tomato = 3 : 5bean height -- 30 cmtomato height -- 50 cmStep-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) = 3/5which 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 cmThe height of the bean plant is 30 cm.The height of the tomato plant is 50 cm._____Alternate solutionWhen 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