Answer :
Let's go through each question step by step and solve them thoroughly.
### Question 18
Problem Statement: If I have two of the same numbers and I add 9, my answer is 21. What is the number?
Solution:
1. Let's denote the unknown number as [tex]\( x \)[/tex].
2. According to the problem, twice the number plus 9 equals 21. This can be written as an equation:
[tex]\[ 2x + 9 = 21 \][/tex]
3. To find the value of [tex]\( x \)[/tex], we need to isolate [tex]\( x \)[/tex]:
[tex]\[ 2x + 9 = 21 \][/tex]
Subtract 9 from both sides:
[tex]\[ 2x + 9 - 9 = 21 - 9 \][/tex]
[tex]\[ 2x = 12 \][/tex]
Divide both sides by 2:
[tex]\[ \frac{2x}{2} = \frac{12}{2} \][/tex]
[tex]\[ x = 6 \][/tex]
So, the number is 6.
### Question 19
Problem Statement: Indicate whether the following is an expression or an equation.
1. [tex]\( -4 + 8 \)[/tex]
2. [tex]\( -9 + 7 = -2 \)[/tex]
Solution:
1. -4 + 8
- This is a mathematical phrase that combines numbers using an arithmetic operation. It does not include an equals sign, which means it is simply a value or an expression.
- Hence, -4 + 8 is an expression.
2. -9 + 7 = -2
- This includes an equals sign and states that one side is equal to the other, making it a complete mathematical statement.
- Therefore, -9 + 7 = -2 is an equation.
### Question 20
Problem Statement: Solve the following by substituting in the value of the variable to make the statements true.
1. If [tex]\( x = 6 \)[/tex] then [tex]\( x - 15 = \)[/tex]
2. If [tex]\( x = -3 \)[/tex], then [tex]\( x + x = \)[/tex]
3. If [tex]\( x = -2 \)[/tex] and [tex]\( y = 5 \)[/tex], then [tex]\( x - y = \)[/tex]
Solution:
1. If [tex]\( x = 6 \)[/tex] then [tex]\( x - 15 = \)[/tex]
[tex]\[ x - 15 = 6 - 15 = -9 \][/tex]
So, the answer is -9.
2. If [tex]\( x = -3 \)[/tex], then [tex]\( x + x = \)[/tex]
[tex]\[ x + x = -3 + (-3) = -6 \][/tex]
So, the answer is -6.
3. If [tex]\( x = -2 \)[/tex] and [tex]\( y = 5 \)[/tex], then [tex]\( x - y = \)[/tex]
[tex]\[ x - y = -2 - 5 = -7 \][/tex]
So, the answer is -7.
### Question 21
Problem Statement: Write an equation using a letter symbol as a placeholder for the unknown number to describe the problem in each of the situations below.
1. There are 40 learners in a class. 34 learners are present and [tex]\( y \)[/tex] learners are absent.
2. Amy has R64 with which to buy popcorn for her and her friends. Each packet of popcorn costs R8. How many packets of popcorn can Amy buy for that amount? Let [tex]\( p \)[/tex] be the number of popcorn packets that Amy can buy.
Solution:
1. There are 40 learners in a class. 34 learners are present and [tex]\( y \)[/tex] learners are absent.
- We know the total number of learners is the sum of the present and absent learners. This can be written as:
[tex]\[ 34 + y = 40 \][/tex]
- This is the required equation.
2. Amy has R64 to buy popcorn. Each packet of popcorn costs R8. How many packets of popcorn can Amy buy for that amount? Let [tex]\( p \)[/tex] be the number of popcorn packets that Amy can buy.
- We know the total cost of [tex]\( p \)[/tex] packets of popcorn is 64 units of money. If each packet costs 8 units of money, we write this as:
[tex]\[ 8p = 64 \][/tex]
- This is the required equation.
I hope these detailed solutions help clarify each question for you!
### Question 18
Problem Statement: If I have two of the same numbers and I add 9, my answer is 21. What is the number?
Solution:
1. Let's denote the unknown number as [tex]\( x \)[/tex].
2. According to the problem, twice the number plus 9 equals 21. This can be written as an equation:
[tex]\[ 2x + 9 = 21 \][/tex]
3. To find the value of [tex]\( x \)[/tex], we need to isolate [tex]\( x \)[/tex]:
[tex]\[ 2x + 9 = 21 \][/tex]
Subtract 9 from both sides:
[tex]\[ 2x + 9 - 9 = 21 - 9 \][/tex]
[tex]\[ 2x = 12 \][/tex]
Divide both sides by 2:
[tex]\[ \frac{2x}{2} = \frac{12}{2} \][/tex]
[tex]\[ x = 6 \][/tex]
So, the number is 6.
### Question 19
Problem Statement: Indicate whether the following is an expression or an equation.
1. [tex]\( -4 + 8 \)[/tex]
2. [tex]\( -9 + 7 = -2 \)[/tex]
Solution:
1. -4 + 8
- This is a mathematical phrase that combines numbers using an arithmetic operation. It does not include an equals sign, which means it is simply a value or an expression.
- Hence, -4 + 8 is an expression.
2. -9 + 7 = -2
- This includes an equals sign and states that one side is equal to the other, making it a complete mathematical statement.
- Therefore, -9 + 7 = -2 is an equation.
### Question 20
Problem Statement: Solve the following by substituting in the value of the variable to make the statements true.
1. If [tex]\( x = 6 \)[/tex] then [tex]\( x - 15 = \)[/tex]
2. If [tex]\( x = -3 \)[/tex], then [tex]\( x + x = \)[/tex]
3. If [tex]\( x = -2 \)[/tex] and [tex]\( y = 5 \)[/tex], then [tex]\( x - y = \)[/tex]
Solution:
1. If [tex]\( x = 6 \)[/tex] then [tex]\( x - 15 = \)[/tex]
[tex]\[ x - 15 = 6 - 15 = -9 \][/tex]
So, the answer is -9.
2. If [tex]\( x = -3 \)[/tex], then [tex]\( x + x = \)[/tex]
[tex]\[ x + x = -3 + (-3) = -6 \][/tex]
So, the answer is -6.
3. If [tex]\( x = -2 \)[/tex] and [tex]\( y = 5 \)[/tex], then [tex]\( x - y = \)[/tex]
[tex]\[ x - y = -2 - 5 = -7 \][/tex]
So, the answer is -7.
### Question 21
Problem Statement: Write an equation using a letter symbol as a placeholder for the unknown number to describe the problem in each of the situations below.
1. There are 40 learners in a class. 34 learners are present and [tex]\( y \)[/tex] learners are absent.
2. Amy has R64 with which to buy popcorn for her and her friends. Each packet of popcorn costs R8. How many packets of popcorn can Amy buy for that amount? Let [tex]\( p \)[/tex] be the number of popcorn packets that Amy can buy.
Solution:
1. There are 40 learners in a class. 34 learners are present and [tex]\( y \)[/tex] learners are absent.
- We know the total number of learners is the sum of the present and absent learners. This can be written as:
[tex]\[ 34 + y = 40 \][/tex]
- This is the required equation.
2. Amy has R64 to buy popcorn. Each packet of popcorn costs R8. How many packets of popcorn can Amy buy for that amount? Let [tex]\( p \)[/tex] be the number of popcorn packets that Amy can buy.
- We know the total cost of [tex]\( p \)[/tex] packets of popcorn is 64 units of money. If each packet costs 8 units of money, we write this as:
[tex]\[ 8p = 64 \][/tex]
- This is the required equation.
I hope these detailed solutions help clarify each question for you!
