Help with missing information problem

[justintime]

Hi,
I am trying to figure this one out. I came up with a solution but would like someone else's perspective:

Figure out how much it snowed in each city assuming each city has different amounts of snow accumulation.

Assume 1 inch = 2.54 centimeters. (numbers in clues are rounded to the nearest hundredth)

1. Paris had 3 times more snow than Montreal.
2. Boston and New York had a total accumulation of eighty-one and twenty-eight hundredths centimeters.
3. Boston and Paris had a total accumulation of seventy-five and twenty-six hundredths centimeters.
4. Boston and Montreal had a total accumulation of twenty-two and fifty-four hundredths inches.

 

[Deleted member 4993]

Hi,
I am trying to figure this one out. I came up with a solution but would like someone else's perspective:

Figure out how much it snowed in each city assuming each city has different amounts of snow accumulation.

Assume 1 inch = 2.54 centimeters. (numbers in clues are rounded to the nearest hundredth)

1. Paris had 3 times more snow than Montreal.
2. Boston and New York had a total accumulation of eighty-one and twenty-eight hundredths centimeters.
3. Boston and Paris had a total accumulation of seventy-five and twenty-six hundredths centimeters.
4. Boston and Montreal had a total accumulation of twenty-two and fifty-four hundredths inches.

Please show us your work .... then comes perspective.....

 

[Denis]

Why are you naming problem this: "Help with missing information problem"??

There is enough information to solve the problem.

 

[justintime]

first I converted all totals to centimeters. So Boston and Montreal have a total of 57.25 cm. (22.54 X 2.54)
Then, Paris is 3 times more than MOntreal, so I'll call it 3m.
1.B + NY + 81.28cm
2. B + Paris (3m) = 75.26cm
3. B + M = 57.25cm
I took the difference between lines 2 and 3 and got 18 cm. (approx)
So then I took 18 and divided it by 3 to get Montreal, since Boston is the same in both lines. I got 6.
So Montreal is 6 cm, Paris is 18cm (3 X 6), But then when I start plugging it in, they don't work.

 

[mmm4444bot]

1.B + NY + 81.28cm

Hi Justintine:

I'm changing your two-character symbol for the centimeters of New York City snow from NY to N, and we can drop the units in our equations.

(1) B + N = 81.28

'

2. B + Paris (3m) = 75.26cm
3. B + M = 57.25cm
I took the difference between lines 2 and 3 and got 18 cm. (approx)
So then I took 18 and divided it by 3 to get Montreal

Paris snowfall is not 18.01 cm.

The difference between snowfall in Paris and Montreal is 18.01 cm.

      B + P = 75.26
  -   B + M = 57.25
  -----------------
      P - M = 18.01

Also, let's hold off any rounding to whole numbers, until the very end. Carrying two decimal places with intermediate results eliminates concerns about round-off error, and the exact solutions (which might turn out to have 3 or more decimal places) could possibly still hold true when rounded to one or two places.

So, we now have the following info (I'll retain your equation numbering):

(1) B + N = 81.28

(2) B + P = 75.26

(3) B + M = 57.25

(4) P = 3M

(5) P - M = 18.01

Journey onward!

Cheers,

~ Mark

Spoiler: Hint, Hint:3ptgb09e

Divide both sides of equation (4) by 3; then look at the result and equation 5 together.[/spoiler:3ptgb09e]

 

[Denis]

B + N = 81.28 [1]
B + P = 75.26 ; -B = P - 75.26 [2]
B + M = 57.25 ; -B = M - 57.25 [3]
P = 3M [4]

Or you can jump right in with [2] and [3]:
P - 75.26 = M - 57.25 ; substitute [4]:
3M - 75.26 = M - 57.25
M = 9.005 = 9.01

That's all you need; go back to get P in [4], then B in [2], then N in [1]

 

[justintime]

Thank you to all!