Grade 6, 7 & 8 Mathematics - Free Printable

Problem: Solve each equation

Below, I will solve each equation step by step. The equations are organized in a grid format, and I will solve them sequentially.

---

#### Equation 1:
\[
\frac{1}{8}b = \frac{7744}{88}
\]

1. Simplify the right-hand side:
\[
\frac{7744}{88} = 88
\]
So the equation becomes:
\[
\frac{1}{8}b = 88
\]

2. Multiply both sides by 8 to isolate \( b \):
\[
b = 88 \times 8 = 704
\]

Solution: \( b = 704 \)

---

#### Equation 2:
\[
x - 66 = 11
\]

1. Add 66 to both sides to isolate \( x \):
\[
x = 11 + 66 = 77
\]

Solution: \( x = 77 \)

---

#### Equation 3:
\[
x - 10 = 5
\]

1. Add 10 to both sides to isolate \( x \):
\[
x = 5 + 10 = 15
\]

Solution: \( x = 15 \)

---

#### Equation 4:
\[
32.1 = a - 21.8
\]

1. Add 21.8 to both sides to isolate \( a \):
\[
a = 32.1 + 21.8 = 53.9
\]

Solution: \( a = 53.9 \)

---

#### Equation 5:
\[
x + \frac{3}{4} = 14
\]

1. Subtract \(\frac{3}{4}\) from both sides to isolate \( x \):
\[
x = 14 - \frac{3}{4}
\]

2. Convert 14 to a fraction with a denominator of 4:
\[
14 = \frac{56}{4}
\]
So:
\[
x = \frac{56}{4} - \frac{3}{4} = \frac{53}{4}
\]

Solution: \( x = \frac{53}{4} \) or \( x = 13.25 \)

---

#### Equation 6:
\[
x + 71 = 160
\]

1. Subtract 71 from both sides to isolate \( x \):
\[
x = 160 - 71 = 89
\]

Solution: \( x = 89 \)

---

#### Equation 7:
\[
-7b = -33.6
\]

1. Divide both sides by -7 to isolate \( b \):
\[
b = \frac{-33.6}{-7} = 4.8
\]

Solution: \( b = 4.8 \)

---

#### Equation 8:
\[
34 = a - 34
\]

1. Add 34 to both sides to isolate \( a \):
\[
a = 34 + 34 = 68
\]

Solution: \( a = 68 \)

---

#### Equation 9:
\[
x + 37 = 99
\]

1. Subtract 37 from both sides to isolate \( x \):
\[
x = 99 - 37 = 62
\]

Solution: \( x = 62 \)

---

#### Equation 10:
\[
n \div 15 = 9
\]

1. Multiply both sides by 15 to isolate \( n \):
\[
n = 9 \times 15 = 135
\]

Solution: \( n = 135 \)

---

#### Equation 11:
\[
68 + 76 = 67 + y
\]

1. Simplify the left-hand side:
\[
68 + 76 = 144
\]
So the equation becomes:
\[
144 = 67 + y
\]

2. Subtract 67 from both sides to isolate \( y \):
\[
y = 144 - 67 = 77
\]

Solution: \( y = 77 \)

---

#### Equation 12:
\[
368 = 46a
\]

1. Divide both sides by 46 to isolate \( a \):
\[
a = \frac{368}{46} = 8
\]

Solution: \( a = 8 \)

---

#### Equation 13:
\[
x + 76 = 132 + 24
\]

1. Simplify the right-hand side:
\[
132 + 24 = 156
\]
So the equation becomes:
\[
x + 76 = 156
\]

2. Subtract 76 from both sides to isolate \( x \):
\[
x = 156 - 76 = 80
\]

Solution: \( x = 80 \)

---

#### Equation 14:
\[
\frac{b}{6} = 5
\]

1. Multiply both sides by 6 to isolate \( b \):
\[
b = 5 \times 6 = 30
\]

Solution: \( b = 30 \)

---

#### Equation 15:
\[
4134.4 = 64.6a
\]

1. Divide both sides by 64.6 to isolate \( a \):
\[
a = \frac{4134.4}{64.6} = 64
\]

Solution: \( a = 64 \)

---

#### Equation 16:
\[
16 + y = 17
\]

1. Subtract 16 from both sides to isolate \( y \):
\[
y = 17 - 16 = 1
\]

Solution: \( y = 1 \)

---

#### Equation 17:
\[
24.78 + y = 27.94
\]

1. Subtract 24.78 from both sides to isolate \( y \):
\[
y = 27.94 - 24.78 = 3.16
\]

Solution: \( y = 3.16 \)

---

#### Equation 18:
\[
\frac{y}{46} = \frac{2208}{276}
\]

1. Simplify the right-hand side:
\[
\frac{2208}{276} = 8
\]
So the equation becomes:
\[
\frac{y}{46} = 8
\]

2. Multiply both sides by 46 to isolate \( y \):
\[
y = 8 \times 46 = 368
\]

Solution: \( y = 368 \)

---

#### Equation 19:
\[
\frac{y}{90} = \frac{51660}{630}
\]

1. Simplify the right-hand side:
\[
\frac{51660}{630} = 82
\]
So the equation becomes:
\[
\frac{y}{90} = 82
\]

2. Multiply both sides by 90 to isolate \( y \):
\[
y = 82 \times 90 = 7380
\]

Solution: \( y = 7380 \)

---

#### Equation 20:
\[
x + \frac{2}{3} = 16
\]

1. Subtract \(\frac{2}{3}\) from both sides to isolate \( x \):
\[
x = 16 - \frac{2}{3}
\]

2. Convert 16 to a fraction with a denominator of 3:
\[
16 = \frac{48}{3}
\]
So:
\[
x = \frac{48}{3} - \frac{2}{3} = \frac{46}{3}
\]

Solution: \( x = \frac{46}{3} \) or \( x = 15.\overline{3} \)

---

#### Equation 21:
\[
\frac{b}{5} = 7.9
\]

1. Multiply both sides by 5 to isolate \( b \):
\[
b = 7.9 \times 5 = 39.5
\]

Solution: \( b = 39.5 \)

---

#### Equation 22:
\[
x + 34 = 11 + 64
\]

1. Simplify the right-hand side:
\[
11 + 64 = 75
\]
So the equation becomes:
\[
x + 34 = 75
\]

2. Subtract 34 from both sides to isolate \( x \):
\[
x = 75 - 34 = 41
\]

Solution: \( x = 41 \)

---

#### Equation 23:
\[
90.5 + y = 141.35
\]

1. Subtract 90.5 from both sides to isolate \( y \):
\[
y = 141.35 - 90.5 = 50.85
\]

Solution: \( y = 50.85 \)

---

#### Equation 24:
\[
x - 21 = 33
\]

1. Add 21 to both sides to isolate \( x \):
\[
x = 33 + 21 = 54
\]

Solution: \( x = 54 \)

---

#### Equation 25:
\[
b \times 14 = 98
\]

1. Divide both sides by 14 to isolate \( b \):
\[
b = \frac{98}{14} = 7
\]

Solution: \( b = 7 \)

---

#### Equation 26:
\[
10 \div c + 11 = 16
\]

1. Subtract 11 from both sides:
\[
10 \div c = 5
\]

2. Rewrite \( 10 \div c \) as \( \frac{10}{c} \):
\[
\frac{10}{c} = 5
\]

3. Multiply both sides by \( c \):
\[
10 = 5c
\]

4. Divide both sides by 5 to isolate \( c \):
\[
c = \frac{10}{5} = 2
\]

Solution: \( c = 2 \)

---

#### Equation 27:
\[
13 + c \times 12 - 18 = 271
\]

1. Simplify the left-hand side:
\[
13 - 18 + c \times 12 = -5 + 12c
\]
So the equation becomes:
\[
-5 + 12c = 271
\]

2. Add 5 to both sides:
\[
12c = 276
\]

3. Divide both sides by 12 to isolate \( c \):
\[
c = \frac{276}{12} = 23
\]

Solution: \( c = 23 \)

---

#### Equation 28:
\[
20 \times (23 \times f) + 5 = 5525
\]

1. Simplify inside the parentheses:
\[
23 \times f = 23f
\]
So the equation becomes:
\[
20 \times 23f + 5 = 5525
\]

2. Simplify further:
\[
460f + 5 = 5525
\]

3. Subtract 5 from both sides:
\[
460f = 5520
\]

4. Divide both sides by 460 to isolate \( f \):
\[
f = \frac{5520}{460} = 12
\]

Solution: \( f = 12 \)

---

#### Equation 29:
\[
(k \div 2) \times 21 = 147
\]

1. Simplify the left-hand side:
\[
\frac{k}{2} \times 21 = \frac{21k}{2}
\]
So the equation becomes:
\[
\frac{21k}{2} = 147
\]

2. Multiply both sides by 2 to eliminate the denominator:
\[
21k = 294
\]

3. Divide both sides by 21 to isolate \( k \):
\[
k = \frac{294}{21} = 14
\]

Solution: \( k = 14 \)

---

#### Equation 30:
\[
j \div 2 = 5
\]

1. Multiply both sides by 2 to isolate \( j \):
\[
j = 5 \times 2 = 10
\]

Solution: \( j = 10 \)

---

Final Answers:

\[
\boxed{
\begin{array}{lll}
1. & b = 704 & 2. & x = 77 & 3. & x = 15 \\
4. & a = 53.9 & 5. & x = \frac{53}{4} & 6. & x = 89 \\
7. & b = 4.8 & 8. & a = 68 & 9. & x = 62 \\
10. & n = 135 & 11. & y = 77 & 12. & a = 8 \\
13. & x = 80 & 14. & b = 30 & 15. & a = 64 \\
16. & y = 1 & 17. & y = 3.16 & 18. & y = 368 \\
19. & y = 7380 & 20. & x = \frac{46}{3} & 21. & b = 39.5 \\
22. & x = 41 & 23. & y = 50.85 & 24. & x = 54 \\
25. & b = 7 & 26. & c = 2 & 27. & c = 23 \\
28. & f = 12 & 29. & k = 14 & 30. & j = 10 \\
\end{array}
}
\]