# Question 1d90b

May 26, 2017

$4.5$ minutes

#### Explanation:

Let's make a ratio:

(60%)/(3) = (100%-10%)/?

That's (60%)/3 = (90%)/?

multiply by $3$ and ? on both sides

60% xx ? = 90% xx 3

convert percentages to decimals

.6 xx ? = .9 xx 3

simplify

.6 xx ?= 2.7

divide by $.6$ on both sides

? = 4.5

So, it would take $4.5$ minutes to burn off 90% of the sugar

May 26, 2017

$4 \frac{1}{2}$ minutes

#### Explanation:

$\textcolor{b l u e}{\text{Preamble}}$

In real life, the actual mechanics of the sugar dissolving in the water has several variables that may influence the rate of it dissolving. This may become very pronounced if the quantity of water is small in comparison to the quantity of sugar.
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$\textcolor{b l u e}{\text{Answering the question}}$

$\textcolor{b r o w n}{\text{Assumption: the rate of dissolving is constant}}$

Using ratio but in fraction format.

Initial condition:" time : percentage "->("time")/("percent")->3/60#

All but 10% means that 90% is dissolved giving:

$\frac{\text{time")/("percent")->3/60 -=("time}}{90}$

Multiply both sides by 90

$\frac{3}{60} \times 90 = \text{ time } \times \frac{90}{90}$

time$\text{ "=" } 4 \frac{1}{2}$ minutes