2005 CEMC Pascal Problems/Problem 6

Problem

A glass filled with water has a mass of $1000 \text{ g}$ . When half the water is removed from the glass, the mass of the glass and the remaining water is $700 \text{ g}$ . What is the mass of the empty glass?

$\text{ (A) }\ 600 \text{ g} \qquad\text{ (B) }\ 500 \text{ g} \qquad\text{ (C) }\ 350 \text{ g} \qquad\text{ (D) }\ 400 \text{ g} \qquad\text{ (E) }\ 300 \text{ g}$

Solution 1

Let $w$ be the mass of the water after half of it is removed, and $g$ be the mass of the glass. We then have:

$2w + g = 1000$ $w + g = 700$

We can just simply solve the system of equations using any method to get the value of $g$ :

$2w + 2g = 700 \times 2 = 1400$

$2w + g = 1000$

$2w + 2g - 2w - g = 1400 - 1000$

$g = \boxed {\textbf {(D) } 400 \text{ g}}$

~anabel.disher

Solution 2 (faster)

We can notice that when half of the water was removed, $1000 - 700 = 300 \text{ g}$ were lost. Getting rid of the rest of the water will leave no water, which gives $700 - 300 = \boxed {\textbf {(D) } 400 \text{ g}}$ for the glass without any water.

~anabel.disher

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2005 CEMC Pascal Problems/Problem 6

Problem

Solution 1

Solution 2 (faster)