Answer :
Sure, let's go through each equation step-by-step and find the solutions:
1. Equation: [tex]\( c \cdot 5 = 65 \cdot 2 \)[/tex]
- Simplify the right side: [tex]\( 65 \cdot 2 = 130 \)[/tex].
- Solve for [tex]\( c \)[/tex]: Divide both sides by 5, giving [tex]\( c = \frac{130}{5} = 26 \)[/tex].
2. Equation: [tex]\( x \cdot 12 = 100 - 28 \)[/tex]
- Simplify the right side: [tex]\( 100 - 28 = 72 \)[/tex].
- Solve for [tex]\( x \)[/tex]: Divide both sides by 12, giving [tex]\( x = \frac{72}{12} = 6 \)[/tex].
3. Equation: [tex]\( \frac{78}{a} = 13 \cdot 3 \)[/tex]
- Simplify the right side: [tex]\( 13 \cdot 3 = 39 \)[/tex].
- Solve for [tex]\( a \)[/tex]: Rearrange the equation to get [tex]\( a = \frac{78}{39} = 2 \)[/tex].
4. Equation: [tex]\( 450 + y = 158 \cdot 4 \)[/tex]
- Simplify the right side: [tex]\( 158 \cdot 4 = 632 \)[/tex].
- Solve for [tex]\( y \)[/tex]: Subtract 450 from both sides, giving [tex]\( y = 632 - 450 = 182 \)[/tex].
5. Equation: [tex]\( 67 + a = 79 \cdot 8 \)[/tex]
- Simplify the right side: [tex]\( 79 \cdot 8 = 632 \)[/tex].
- Solve for [tex]\( a \)[/tex]: Subtract 67 from both sides, giving [tex]\( a = 632 - 67 = 565 \)[/tex].
6. Equation: [tex]\( 600 + y = 219 \cdot 4 \)[/tex]
- Simplify the right side: [tex]\( 219 \cdot 4 = 876 \)[/tex].
- Solve for [tex]\( y \)[/tex]: Subtract 600 from both sides, giving [tex]\( y = 876 - 600 = 276 \)[/tex].
7. Equation: [tex]\( \frac{52}{x} = \frac{48}{12} \)[/tex]
- Simplify the right side: [tex]\( \frac{48}{12} = 4 \)[/tex].
- Solve for [tex]\( x \)[/tex]: Rearrange the equation to get [tex]\( x = \frac{52}{4} = 13 \)[/tex].
8. Equation: [tex]\( x + 230 = 450 + 210 + 70 \)[/tex]
- Simplify the right side: [tex]\( 450 + 210 + 70 = 730 \)[/tex].
- Solve for [tex]\( x \)[/tex]: Subtract 230 from both sides, giving [tex]\( x = 730 - 230 = 500 \)[/tex].
These are the solutions for the respective equations:
1. [tex]\( c = 26 \)[/tex]
2. [tex]\( x = 6 \)[/tex]
3. [tex]\( a = 2 \)[/tex]
4. [tex]\( y = 182 \)[/tex]
5. [tex]\( a = 565 \)[/tex]
6. [tex]\( y = 276 \)[/tex]
7. [tex]\( x = 13 \)[/tex]
8. [tex]\( x = 500 \)[/tex]
1. Equation: [tex]\( c \cdot 5 = 65 \cdot 2 \)[/tex]
- Simplify the right side: [tex]\( 65 \cdot 2 = 130 \)[/tex].
- Solve for [tex]\( c \)[/tex]: Divide both sides by 5, giving [tex]\( c = \frac{130}{5} = 26 \)[/tex].
2. Equation: [tex]\( x \cdot 12 = 100 - 28 \)[/tex]
- Simplify the right side: [tex]\( 100 - 28 = 72 \)[/tex].
- Solve for [tex]\( x \)[/tex]: Divide both sides by 12, giving [tex]\( x = \frac{72}{12} = 6 \)[/tex].
3. Equation: [tex]\( \frac{78}{a} = 13 \cdot 3 \)[/tex]
- Simplify the right side: [tex]\( 13 \cdot 3 = 39 \)[/tex].
- Solve for [tex]\( a \)[/tex]: Rearrange the equation to get [tex]\( a = \frac{78}{39} = 2 \)[/tex].
4. Equation: [tex]\( 450 + y = 158 \cdot 4 \)[/tex]
- Simplify the right side: [tex]\( 158 \cdot 4 = 632 \)[/tex].
- Solve for [tex]\( y \)[/tex]: Subtract 450 from both sides, giving [tex]\( y = 632 - 450 = 182 \)[/tex].
5. Equation: [tex]\( 67 + a = 79 \cdot 8 \)[/tex]
- Simplify the right side: [tex]\( 79 \cdot 8 = 632 \)[/tex].
- Solve for [tex]\( a \)[/tex]: Subtract 67 from both sides, giving [tex]\( a = 632 - 67 = 565 \)[/tex].
6. Equation: [tex]\( 600 + y = 219 \cdot 4 \)[/tex]
- Simplify the right side: [tex]\( 219 \cdot 4 = 876 \)[/tex].
- Solve for [tex]\( y \)[/tex]: Subtract 600 from both sides, giving [tex]\( y = 876 - 600 = 276 \)[/tex].
7. Equation: [tex]\( \frac{52}{x} = \frac{48}{12} \)[/tex]
- Simplify the right side: [tex]\( \frac{48}{12} = 4 \)[/tex].
- Solve for [tex]\( x \)[/tex]: Rearrange the equation to get [tex]\( x = \frac{52}{4} = 13 \)[/tex].
8. Equation: [tex]\( x + 230 = 450 + 210 + 70 \)[/tex]
- Simplify the right side: [tex]\( 450 + 210 + 70 = 730 \)[/tex].
- Solve for [tex]\( x \)[/tex]: Subtract 230 from both sides, giving [tex]\( x = 730 - 230 = 500 \)[/tex].
These are the solutions for the respective equations:
1. [tex]\( c = 26 \)[/tex]
2. [tex]\( x = 6 \)[/tex]
3. [tex]\( a = 2 \)[/tex]
4. [tex]\( y = 182 \)[/tex]
5. [tex]\( a = 565 \)[/tex]
6. [tex]\( y = 276 \)[/tex]
7. [tex]\( x = 13 \)[/tex]
8. [tex]\( x = 500 \)[/tex]
