Let's solve each equation step by step.
Equation: \( X \cdot 30 + 90 = 1200 \)
\[ X \cdot 30 = 1200 - 90 \] \[ X \cdot 30 = 1110 \] \[ X = \frac{1110}{30} = 37 \]
Equation: \( X \cdot (30 + 90) = 1200 \)
\[ X \cdot 120 = 1200 \] \[ X = \frac{1200}{120} = 10 \]
Equation: \( (750 - 25) \cdot y = 0 \)
\[ 725 \cdot y = 0 \] The only solution is \( y = 0 \).
Equation: \( 750 - 25 \cdot y = 0 \)
\[ 750 = 25 \cdot y \] \[ y = \frac{750}{25} = 30 \]
Equation: \( 86 + x + 138 = 250 \)
\[ x + 224 = 250 \] \[ x = 250 - 224 = 26 \]
Equation: \( 452 + y - 230 = 222 \)
\[ 452 - 230 + y = 222 \] \[ 222 + y = 222 \implies y = 0 \]
Equation: \( (5 \times 19) \cdot x = 3800 \times 20 \)
\[ 95x = 76000 \] \[ x = \frac{76000}{95} = 800 \]
Equation: \( \frac{18 \times 9}{x} = \frac{324}{4} \)
\[ \frac{162}{x} = 81 \] \[ 162 = 81x \implies x = \frac{162}{81} = 2 \]
Equation: \( 5 \times 5 - 2 \times 2 \times 2 + x = 7 \times 7 \)
\[ 25 - 16 + x = 49 \] \[ x = 49 - 9 = 40 \]
Equation: \( 4 \times 4 \cdot 2 \times 2 \times 2 \times 2 \times 2 - x = 3 \times 3 \)
\[ 64 - x = 9 \] \[ x = 64 - 9 = 55 \]
Equation: \( 168 \cdot x \cdot 5 = 2520 \)
\[ 840x = 2520 \] \[ x = \frac{2520}{840} = 3 \]
Equation: \( 221 \cdot 3 \cdot 15 = 13260 \)
This equation is already satisfied.
Equation: \( \frac{93}{3} \div x = 31 \)
\[ 31 \div x = 31 \implies x = 1 \]
Equation: \( \frac{128}{4} \div y = 16 \)
\[ 32 \div y = 16 \implies y = 2 \]
Equation: \( 250(175 - y) = 125 \)
\[ 175 - y = \frac{125}{250} = 0.5 \] \[ y = 175 - 0.5 = 174.5 \]
Equation: \( 629 - (333 - y) = 459 \)
\[ 629 - 333 + y = 459 \] \[ y = 459 - 296 = 163 \]
Equation: \( (y + 100) - 60 = 240 \)
\[ y + 40 = 240 \] \[ y = 200 \]
Summary of Solutions:
- \( X = 37 \)
- \( X = 10 \)
- \( y = 0 \)
- \( y = 30 \)
- \( x = 26 \)
- \( y = 0 \)
- \( x = 800 \)
- \( x = 2 \)
- \( x = 40 \)
- \( x = 55 \)
- \( x = 3 \)
- Equation is true (not a variable)
- \( x = 1 \)
- \( y = 2 \)
- \( y = 174.5 \)
- \( y = 163 \)
- \( y = 200 \)