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What is the value of the expression shown below, given the three equations?

Mathematics

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Answer

52\text{52}

Step-by-step solution

4 steps
  1. Determine the value of the triangle (△\triangle).

    From the first equation, three triangles sum to 30.

    △+△+△=30\triangle + \triangle + \triangle = 30 3×△=303 \times \triangle = 30 △=303\triangle = \frac{30}{3} △=10\triangle = 10
  2. Determine the value of the square (□\square).

    Substitute the value of △\triangle into the second equation.

    △+□+□=20\triangle + \square + \square = 20 10+2×□=2010 + 2 \times \square = 20 2×□=20−102 \times \square = 20 - 10 2×□=102 \times \square = 10 □=102\square = \frac{10}{2} □=5\square = 5
  3. Determine the value of the circle (◯\bigcirc).

    Substitute the value of □\square into the third equation.

    □+◯+◯=9\square + \bigcirc + \bigcirc = 9 5+2×◯=95 + 2 \times \bigcirc = 9 2×◯=9−52 \times \bigcirc = 9 - 5 2×◯=42 \times \bigcirc = 4 ◯=42\bigcirc = \frac{4}{2} ◯=2\bigcirc = 2
  4. Calculate the final expression.

    Substitute the values of ◯\bigcirc, △\triangle, and □\square into the final expression, remembering the order of operations (multiplication before addition).

    ◯+△×□=?\bigcirc + \triangle \times \square = ? 2+10×52 + 10 \times 5 2+502 + 50 =52= 52

    The final answer is 52\text{52}.

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