Certainly! Let's set up and solve the equations for each of the given scenarios step-by-step.
---
### Part (i): Add 4 to 5 times a number to get 64.
1. Set Up the Equation:
Let the unknown number be [tex]\( x \)[/tex].
The equation is [tex]\( 5x + 4 = 64 \)[/tex].
2. Isolate [tex]\( x \)[/tex]:
Subtract 4 from both sides:
[tex]\[
5x = 64 - 4
\][/tex]
Simplify the right-hand side:
[tex]\[
5x = 60
\][/tex]
Divide both sides by 5:
[tex]\[
x = \frac{60}{5}
\][/tex]
[tex]\[
x = 12
\][/tex]
So, the number is [tex]\( x = 12 \)[/tex].
---
### Part (ii): Nine less than one-half a number is fourteen.
1. Set Up the Equation:
Let the unknown number be [tex]\( x \)[/tex].
The equation is [tex]\( \frac{1}{2}x - 9 = 14 \)[/tex].
2. Isolate [tex]\( x \)[/tex]:
Add 9 to both sides:
[tex]\[
\frac{1}{2}x = 14 + 9
\][/tex]
Simplify the right-hand side:
[tex]\[
\frac{1}{2}x = 23
\][/tex]
Multiply both sides by 2:
[tex]\[
x = 2 \times 23
\][/tex]
[tex]\[
x = 46
\][/tex]
So, the number is [tex]\( x = 46 \)[/tex].
---
### Part (iii): Ten decreased by twice a number is two.
1. Set Up the Equation:
Let the unknown number be [tex]\( x \)[/tex].
The equation is [tex]\( 10 - 2x = 2 \)[/tex].
2. Isolate [tex]\( x \)[/tex]:
Subtract 10 from both sides:
[tex]\[
-2x = 2 - 10
\][/tex]
Simplify the right-hand side:
[tex]\[
-2x = -8
\][/tex]
Divide both sides by -2:
[tex]\[
x = \frac{-8}{-2}
\][/tex]
[tex]\[
x = 4
\][/tex]
So, the number is [tex]\( x = 4 \)[/tex].
---
### Part (iv): When I subtract 2 from 8 times a number, I get 22.
1. Set Up the Equation:
Let the unknown number be [tex]\( x \)[/tex].
The equation is [tex]\( 8x - 2 = 22 \)[/tex].
2. Isolate [tex]\( x \)[/tex]:
Add 2 to both sides:
[tex]\[
8x = 22 + 2
\][/tex]
Simplify the right-hand side:
[tex]\[
8x = 24
\][/tex]
Divide both sides by 8:
[tex]\[
x = \frac{24}{8}
\][/tex]
[tex]\[
x = 3
\][/tex]
So, the number is [tex]\( x = 3 \)[/tex].
---
### Part (v): Sita thinks of a number. If she adds 19 to it and divides the sum by 5, she will get 8.
1. Set Up the Equation:
Let the unknown number be [tex]\( x \)[/tex].
The equation is [tex]\( \frac{x + 19}{5} = 8 \)[/tex].
2. Isolate [tex]\( x \)[/tex]:
Multiply both sides by 5:
[tex]\[
x + 19 = 8 \times 5
\][/tex]
Simplify the right-hand side:
[tex]\[
x + 19 = 40
\][/tex]
Subtract 19 from both sides:
[tex]\[
x = 40 - 19
\][/tex]
[tex]\[
x = 21
\][/tex]
So, the number is [tex]\( x = 21 \)[/tex].
---
In summary, the numbers are:
- (i) [tex]\( 12 \)[/tex]
- (ii) [tex]\( 46 \)[/tex]
- (iii) [tex]\( 4 \)[/tex]
- (iv) [tex]\( 3 \)[/tex]
- (v) [tex]\( 21 \)[/tex]
I hope this helps! If you have any more questions, feel free to ask.
