Answer :
Certainly! Let's solve each of these equations step-by-step:
1. Equation 1: [tex]\( c \cdot 5 = 65 \cdot 2 \)[/tex]
To find [tex]\( c \)[/tex], divide both sides by 5:
[tex]\[
c = \frac{65 \cdot 2}{5} = 26.0
\][/tex]
2. Equation 2: [tex]\( x \cdot 12 = 100 - 28 \)[/tex]
First, simplify the right side:
[tex]\[
x \cdot 12 = 72
\][/tex]
Then, divide by 12 to find [tex]\( x \)[/tex]:
[tex]\[
x = \frac{72}{12} = 6.0
\][/tex]
3. Equation 3: [tex]\( \frac{78}{a} = 13 \cdot 3 \)[/tex]
Simplify the right side:
[tex]\[
\frac{78}{a} = 39
\][/tex]
Then, solve for [tex]\( a \)[/tex]:
[tex]\[
a = \frac{78}{39} = 2.0
\][/tex]
4. Equation 4: [tex]\( 450 + y = 158 \cdot 4 \)[/tex]
Simplify the right side:
[tex]\[
450 + y = 632
\][/tex]
Solve for [tex]\( y \)[/tex]:
[tex]\[
y = 632 - 450 = 182
\][/tex]
5. Equation 5: [tex]\( 67 + a = 79 \cdot 8 \)[/tex]
Simplify the right side:
[tex]\[
67 + a = 632
\][/tex]
Solve for [tex]\( a \)[/tex]:
[tex]\[
a = 632 - 67 = 565
\][/tex]
6. Equation 6: [tex]\( 600 + y = 219 \cdot 4 \)[/tex]
Simplify the right side:
[tex]\[
600 + y = 876
\][/tex]
Solve for [tex]\( y \)[/tex]:
[tex]\[
y = 876 - 600 = 276
\][/tex]
7. Equation 7: [tex]\( \frac{52}{x} = \frac{48}{12} \)[/tex]
Simplify the right side:
[tex]\[
\frac{48}{12} = 4
\][/tex]
Then solve for [tex]\( x \)[/tex]:
[tex]\[
x = \frac{52}{4} = 13.0
\][/tex]
8. Equation 8: [tex]\( x + 230 = 450 + 210 + 70 \)[/tex]
Simplify the right side:
[tex]\[
x + 230 = 730
\][/tex]
Solve for [tex]\( x \)[/tex]:
[tex]\[
x = 730 - 230 = 500
\][/tex]
These are the solutions for each equation:
- [tex]\( c = 26.0 \)[/tex]
- [tex]\( x = 6.0 \)[/tex] (from Equation 2)
- [tex]\( a = 2.0 \)[/tex]
- [tex]\( y = 182 \)[/tex] (from Equation 4)
- [tex]\( a = 565 \)[/tex] (from Equation 5)
- [tex]\( y = 276 \)[/tex] (from Equation 6)
- [tex]\( x = 13.0 \)[/tex] (from Equation 7)
- [tex]\( x = 500 \)[/tex] (from Equation 8)
1. Equation 1: [tex]\( c \cdot 5 = 65 \cdot 2 \)[/tex]
To find [tex]\( c \)[/tex], divide both sides by 5:
[tex]\[
c = \frac{65 \cdot 2}{5} = 26.0
\][/tex]
2. Equation 2: [tex]\( x \cdot 12 = 100 - 28 \)[/tex]
First, simplify the right side:
[tex]\[
x \cdot 12 = 72
\][/tex]
Then, divide by 12 to find [tex]\( x \)[/tex]:
[tex]\[
x = \frac{72}{12} = 6.0
\][/tex]
3. Equation 3: [tex]\( \frac{78}{a} = 13 \cdot 3 \)[/tex]
Simplify the right side:
[tex]\[
\frac{78}{a} = 39
\][/tex]
Then, solve for [tex]\( a \)[/tex]:
[tex]\[
a = \frac{78}{39} = 2.0
\][/tex]
4. Equation 4: [tex]\( 450 + y = 158 \cdot 4 \)[/tex]
Simplify the right side:
[tex]\[
450 + y = 632
\][/tex]
Solve for [tex]\( y \)[/tex]:
[tex]\[
y = 632 - 450 = 182
\][/tex]
5. Equation 5: [tex]\( 67 + a = 79 \cdot 8 \)[/tex]
Simplify the right side:
[tex]\[
67 + a = 632
\][/tex]
Solve for [tex]\( a \)[/tex]:
[tex]\[
a = 632 - 67 = 565
\][/tex]
6. Equation 6: [tex]\( 600 + y = 219 \cdot 4 \)[/tex]
Simplify the right side:
[tex]\[
600 + y = 876
\][/tex]
Solve for [tex]\( y \)[/tex]:
[tex]\[
y = 876 - 600 = 276
\][/tex]
7. Equation 7: [tex]\( \frac{52}{x} = \frac{48}{12} \)[/tex]
Simplify the right side:
[tex]\[
\frac{48}{12} = 4
\][/tex]
Then solve for [tex]\( x \)[/tex]:
[tex]\[
x = \frac{52}{4} = 13.0
\][/tex]
8. Equation 8: [tex]\( x + 230 = 450 + 210 + 70 \)[/tex]
Simplify the right side:
[tex]\[
x + 230 = 730
\][/tex]
Solve for [tex]\( x \)[/tex]:
[tex]\[
x = 730 - 230 = 500
\][/tex]
These are the solutions for each equation:
- [tex]\( c = 26.0 \)[/tex]
- [tex]\( x = 6.0 \)[/tex] (from Equation 2)
- [tex]\( a = 2.0 \)[/tex]
- [tex]\( y = 182 \)[/tex] (from Equation 4)
- [tex]\( a = 565 \)[/tex] (from Equation 5)
- [tex]\( y = 276 \)[/tex] (from Equation 6)
- [tex]\( x = 13.0 \)[/tex] (from Equation 7)
- [tex]\( x = 500 \)[/tex] (from Equation 8)
