The Ratio of the hieght of plant X to plant Y is 5:3. If plant Y were 140 c.m. taller instead, the ratio of the hieght of plant X to plant Y would be 1:2. How tall is plant X
Translate these info into equations:
y=3/5x
x=5/3y
y+140=2x
Now you can use substitution method to solve for x easily.
alternate solution:
let the height of pant X be 5x
let the height of plant Y be 3x
5x/(3x+140) = 1/2
10x = 3x+140
x= 20
then X = 5x = 100
Y = 3x = 60
check : if 140 is added to 60, Y = 200
then X:Y = 1:2
To solve this problem, we can set up a system of equations based on the given information.
Let's say the initial height of plant X is 5x cm, and the initial height of plant Y is 3x cm.
According to the first part of the problem, the ratio of plant X to plant Y is 5:3. Thus, we have the equation:
(Height of X) / (Height of Y) = 5/3
(5x) / (3x) = 5/3
Now, in the second part of the problem, if plant Y were 140 cm taller, the ratio of plant X to plant Y becomes 1:2. This gives us another equation:
(Height of X) / (Height of Y + 140) = 1/2
(5x) / (3x + 140) = 1/2
To solve this system of equations, we can cross-multiply and solve for x:
(5x) / (3x) = 5/3
Cross-multiply: 5x * 3x = 5 * 3x
15x^2 = 15x
(5x) / (3x + 140) = 1/2
Cross-multiply: 5x * 2 = 1 * (3x + 140)
10x = 3x + 140
7x = 140
x = 20
Now, we can substitute the value of x into the equation for the height of plant X:
Height of X = 5x
Height of X = 5 * 20
Height of X = 100 cm
Therefore, plant X is 100 cm tall.