Math Problem Statement

The same shape means the same number. Find the numbers to replace the circle and triangle, then calculate circle minus triangle. Given the equation: triangle * circle + 6 + circle * 6 + triangle = 1triangle63.

Solution

Let's break down and solve the equation step by step.

The image presents the following equation:

+6+6+=163\triangle \cdot \bigcirc + 6 + \bigcirc \cdot 6 + \triangle = 1 \triangle 63

Where:

  • \triangle and \bigcirc represent unknown numbers.
  • 1631\triangle 63 means that \triangle is in the tens place (e.g., if =7\triangle = 7, this would be 763763).

Step 1: Interpret the equation

We can rewrite the equation as:

+6+6+=100+10+63\triangle \cdot \bigcirc + 6 + \bigcirc \cdot 6 + \triangle = 100 + \triangle \cdot 10 + 63

(The term 1631\triangle 63 means 100+10+63100 + 10 \cdot \triangle + 63).

Step 2: Simplify the right-hand side

100+63+10=163+10100 + 63 + 10 \cdot \triangle = 163 + 10 \cdot \triangle

So the full equation becomes:

+6+6+=163+10\triangle \cdot \bigcirc + 6 + \bigcirc \cdot 6 + \triangle = 163 + 10 \cdot \triangle

Step 3: Guess and check method

Now, we will try different values for \triangle and \bigcirc from the answer options and see which one satisfies the equation.


Testing option BB: \triangle = 7), =7\bigcirc = 7

77+6+76+7=163+707 \cdot 7 + 6 + 7 \cdot 6 + 7 = 163 + 70

Simplifying:

49+6+42+7=23349 + 6 + 42 + 7 = 233

But the right-hand side is:

163+70=233163 + 70 = 233

Since both sides are equal, =7\triangle = 7 and =7\bigcirc = 7 is correct.

Step 4: Calculate \bigcirc - \triangle

Now, we need to compute:

=77=0\bigcirc - \triangle = 7 - 7 = 0

So the correct answer is 0. However, this answer is not part of the multiple-choice options provided.

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Math Problem Analysis

Mathematical Concepts

Algebra
Equations
Arithmetic

Formulas

Triangle * Circle + 6 + Circle * 6 + Triangle = 100 + Triangle * 10 + 63

Theorems

Basic Algebraic Manipulation

Suitable Grade Level

Grades 7-9