The heights of three plants A,B and C in a garden are in the ratio 2 : 3 :5. their mean height is 30cm
a) find the height of plant b
b) if another plant D is added to the garden and the mean height of the four plant is now 33cm , find the height of D plant
the mean of 2,3,5 is 10/3
So, to have a mean height of 30, each number must be multiplied by 9, giving heights in the ratios
18:27:45
If 4 plants have a mean of 33, their sum is 4*33 = 132
18+27+45=90, so the 4th plant has height 42
2k + 3k + 5k = 3 * 30 cm
10k = 90 cm ... k = 10 cm
a) 3 * k = 30 cm
b) 90 cm + D = 4 * 33 cm ... D = 42 cm
oops...
k = 9
3k = 27
To solve this problem, we will use the concept of ratios and means.
a) To find the height of plant B, we need to know the value of the ratio. The heights of A, B, and C are in the ratio 2:3:5. Assuming the height of plant B is represented by 3x, where x is a constant, we can set up the equation:
2x + 3x + 5x = 30
10x = 30
x = 3
Now, we can find the height of plant B:
Height of plant B = 3x = 3 * 3 = 9 cm
Therefore, the height of plant B is 9 cm.
b) We need to find the height of plant D. Given that the mean height of the four plants is 33 cm, we can set up the equation:
(2x + 3x + 5x + D) / 4 = 33
To solve this equation, we can substitute the value of x we found in part a:
(2*3 + 3*3 + 5*3 + D) / 4 = 33
(6 + 9 + 15 + D) / 4 = 33
(30 + D) / 4 = 33
To isolate D, we can multiply both sides of the equation by 4:
30 + D = 33 * 4
30 + D = 132
Now, subtract 30 from both sides of the equation:
D = 132 - 30
D = 102
Therefore, the height of plant D is 102 cm.