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siniylev [52]
3 years ago
15

Jackson and derek have a lemonade stand. They sell lemonade in 12oz cups. They are hoping to sell at least 50 cups of lemonade.

Jackson says that they should make 5 gallons, but derek thinks that 17 quarts of lemonade will be enough. Whose amount will give them enough lemonade to fill 50 12oz cups ?
Mathematics
1 answer:
siniylev [52]3 years ago
5 0

To fill 50 12-fl oz cups, you need 50 * 12 fl oz = 600 fl oz

There are 128 fl oz in a gallon

600/128 = 4.6875

600 fl oz = 4.6875 gallons

600 fl oz is under 5 gallons, so 5 gallons is enough.

1 qt = 32 fl oz

17 qt = 17 * 32 fl oz = 544 fl oz

17 quarts is 544 fl oz, which is under the needed 600 fl oz, so 17 quarts is not enough.

Answer: 5 gallons

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A pan of warm water (46∘ Celsius) was put in a refrigerator. After 15 minutes, the water's temperature was 27∘ C; 15 minutes aft
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The refrigerator was at around 13 ∘C

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Newton's Law of Cooling:

The rate of change of a body temperature  (amount of heat loss/time of loss) is directly proportional to the difference between its own temperature and the surroundings.

\frac{T(t2)-T(t1)}{t2-t1} = -h (T(t2) - Tenv)

T ⇒ temperature

t ⇒ time

Tenv ⇒refrigerator temperature

\frac{T(t2)-T(t1)}{t2-t1} ⇒ rate of change of he temperature

-h ⇒ constant of proportionality (negative because the temperature is decreasing inside the refrigerator)

We have 3 points:

time (minutes) - Temperature (∘ C)

0 (when the pan was put in the refrigerator) - 46

15 (after 15 minutes) - 27

30 (15 minutes after the first 15 minutes) - 19

\frac{27 - 46}{15 - 0} = -h (27 - Tenv)

\frac{19 - 27}{15 - 0} = -h (19 - Tenv)

Now we have a system of two equations and two variables

\frac{-19}{15} = -h (27 - Tenv)\\ \frac{19}{15} = h (27 - Tenv)\\ \frac{19}{15(27 - Tenv)} = h

\frac{19 - 27}{15 - 0} = -h (19 - Tenv)\\\frac{-8}{15} = -h (19 - Tenv)\\\frac{8}{15} = h (19 - Tenv)\\\frac{8}{15} = \frac{19}{15(27 - Tenv)} (19 - Tenv)\\8(27 - Tenv) = 19 (19 - Tenv)\\216 - 8 Tenv = 361 - 19 Tenv\\19 Tenv - 8 Tenv = 361 - 216\\11 Tenv = 145 \\Tenv = 145/ 11\\Tenv = 13. 18

The refrigerator was at around 13 ∘C

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