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?
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.
To find the combined height of Mo, Liz, and Dee, we need to determine the height ratios of Liz and Dee compared to Mo.
First, let's set up the ratio using the information given:
Mo's height = 144cm
Mo's height ratio = 32
To find Liz's height ratio, we can set up a proportion:
Mo's height ratio / Liz's height ratio = Mo's height / Liz's height
Substituting the known values:
32 / Liz's height ratio = 144 / Liz's height
To solve for Liz's height ratio, we can cross-multiply:
32 * Liz's height = 144 * Liz's height ratio
Now, we can solve for Liz's height by dividing both sides of the equation by Liz's height ratio:
Liz's height = (144 * Liz's height ratio) / 32
To find Dee's height ratio, we can use a similar approach:
Mo's height ratio / Dee's height ratio = Mo's height / Dee's height
Substituting the known values:
32 / Dee's height ratio = 144 / Dee's height
Again, we can cross-multiply to solve for Dee's height ratio:
32 * Dee's height = 144 * Dee's height ratio
Solving for Dee's height, we divide both sides of the equation by Dee's height ratio:
Dee's height = (144 * Dee's height ratio) / 32
Finally, to find the combined height of Mo, Liz, and Dee, we add up their heights:
Combined height = Mo's height + Liz's height + Dee's height
To find the combined height of Mo, Liz, and Dee, we need to determine the heights of Liz and Dee first. We are given that Mo's height is 144 cm and that the heights are in the ratio 32:33:37.
Let's use a proportion to find the heights of Liz and Dee. Since Mo's height is given as 144 cm, we can set up a proportion using the ratio:
32:33 = 144:X
To solve this proportion, we can cross-multiply:
32X = 33 * 144
Now we can divide both sides of the equation by 32 to solve for X:
X = (33 * 144) / 32
Calculating this expression gives us X ≈ 148.5 cm. This is Liz's height.
To find Dee's height, we use another proportion:
33:37 = 148.5:Y
Cross-multiplying and solving for Y:
33Y = 37 * 148.5
Dividing both sides by 33 gives us:
Y = (37 * 148.5) / 33
Calculating this expression gives us Y ≈ 166.5 cm. This is Dee's height.
Now that we have the heights of all three people, we can find the combined height by adding them together:
Combined height = Mo's height + Liz's height + Dee's height
= 144 cm + 148.5 cm + 166.5 cm
≈ 459 cm
Therefore, the combined height of Mo, Liz, and Dee is approximately 459 cm.