Question

Heights of andy and michael are in the ratio 4 : 3 and the heights of michael and jim are in the ratio of 5 : 6. what is jim's height (in if the sum of the heights of all three is 530 cm?

a. 170
b. 180
c. 165
d. 200

Answer 1

Using the given ratios and the total height, we expressed the heights in terms of variables and equations, which allowed us to solve for Jim's height to be 180 cm.

Step-by-step explanation:

The question asks us to find Jim's height given the ratios of Andy's height to Michael's, and Michael's to Jim's, along with the total height of all three. We can solve this problem using a system of equations based on these ratios and the total height.

Let's denote Andy's height as 4x, Michael's height as 3x (since their ratio is 4:3), and Michael's height as 5y, and Jim's height as 6y (since their ratio is 5:6). We know that the sum of their heights (4x + 3x + 6y) equals 530 cm.

Firstly, since Michael is common to both ratios, we can equate 3x to 5y. By rearranging this equation, we can express y in terms of x (y = 3x/5).

Now we can substitute y in our original total height equation:

1. 4x + 3x + 6(3x/5) = 530
2. Simplify the equation: 4x + 3x + 18x/5 = 530
3. Combine like terms: (20x + 15x + 18x)/5 = 530
4. Multiply through by 5 to clear the denominator: 20x + 15x + 18x = 2650
5. Add the x terms: 53x = 2650
6. Divide by 53 to solve for x: x = 50
7. Now, find Jim's height by multiplying y by 6: Jim's Height = 6y = 6(3x/5) = 6(3*50/5) = 6*30 = 180 cm

Therefore, Jim's height is 180 cm, which corresponds to option b.