2006 CEMC Pascal Problems/Problem 7

Problem

In the diagram, two equal-armed balances are shown.

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How many () would it take to balance ()?

$\text{ (A) }\ 2 \qquad\text{ (B) }\ 1 \qquad\text{ (C) }\ 4 \qquad\text{ (D) }\ 5 \qquad\text{ (E) }\ 3$

Solution

Using the balance found on the left part of the diagram, we can see that $1$ triangle weighs the same as $2$ squares. This means that $2$ triangles would weigh the same as $2 \times 2 = 4$ squares.

Since $2$ triangles weighs the same as $4$ squares, and $2$ triangles also weigh the same as $3$ circles, we can conclude that $4$ squares weigh the same as $\boxed {\textbf {(E) } 3}$ circles.

~anabel.disher

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2006 CEMC Pascal Problems/Problem 7

Problem

Solution