Ratios

Mo, Liz and Dee's heights are in the the ratio 32:33:37. Mo is 144cm tall.
What is the combined height of the three people?

5 answers

We can start by setting up a proportion using Mo's height as the known value and the given ratio:

32:33:37 = 144:x:y

To solve for x and y, we can cross-multiply:

32y = 33x
37x = 32 * 144

Simplifying the second equation:

x = 32 * 144 / 37
x = 124.22 (rounded to two decimal places)

Now we can substitute x back into the first equation to solve for y:

32y = 33 * 124.22
y = 128.66 (rounded to two decimal places)

To find the combined height of all three people, we add up their heights:

144 + 124.22 + 128.66 = 397.88

Therefore, the combined height of Mo, Liz, and Dee is approximately 397.88 cm.
Max, Molly and Maisie are at a bus stop. The number of minutes they have waited can be represented by the ratio 3:7:2. Molly has been waiting for 1 hour and 10 minutes.
How long have Max and Maisie been waiting
We can start by converting Molly's waiting time into minutes:

1 hour = 60 minutes
1 hour and 10 minutes = 70 minutes

We can then set up a proportion using Molly's waiting time as the known value and the given ratio:

3:7:2 = x:70:y

To solve for x and y, we can cross-multiply:

3y = 70x
2x = 7 * 70

Simplifying the second equation:

x = 490 / 2
x = 245

Now we can substitute x back into the first equation to solve for y:

3y = 70 * 245
y = 4900 / 3
y = 1633.33 (rounded to two decimal places)

Since the question is asking for Max and Maisie's waiting time, we only need to find the values of x and y. Therefore, Max has been waiting for 245 minutes and Maisie has been waiting for 1633.33 (or approximately 1633) minutes.
AAAaannndd the bot gets it wrong yet again!

144/32 = 4.5, so
4.5(32+33+37) = 459 cm
You are correct, and I apologize for the mistake in my previous response. The correct method is to divide Mo's height (144 cm) by the first ratio value (32) to find the common ratio factor:

144/32 = 4.5

Then, we multiply this factor by the sum of all three ratio values to find the combined height of the three people:

4.5 * (32 + 33 + 37) = 459 cm

Therefore, the combined height of Mo, Liz, and Dee is 459 cm. Thank you for pointing out the error.
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