Problem 23 · 2009 Math Kangaroo
Stretch
Algebra & Patterns
substitutioncasework
In the diagram the total of each row and each column is given. What is the value of the spiral symbol?
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Answer: A — 3
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Hint 1 of 2
Give each symbol a letter and turn the row and column totals into equations.
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Hint 2 of 2
Use a row or column with the asked symbol and two knowns to solve for it.
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Approach: solve the symbol equations
- Let the black square = s, the spiral = l, the triangle = t.
- Top row s + l + s = 11 and a column s + l + l = 10; with the other totals these give s = 4, t = 1.
- Substituting back, the spiral l = 3.
- So the spiral's value is 3 — answer A.
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