Let's solve each problem step by step:
1. A number multiplied by 7, and 15 subtracted from the product gives 20.
- Let the number be [tex]\( x \)[/tex].
- The equation is: [tex]\( 7x - 15 = 20 \)[/tex].
- To find [tex]\( x \)[/tex], solve the equation:
[tex]\[
7x - 15 = 20
\][/tex]
Add 15 to both sides:
[tex]\[
7x = 35
\][/tex]
Divide by 7:
[tex]\[
x = 5
\][/tex]
2. Charmaine is [tex]\( x \)[/tex] years old and in 14 years she will be twenty-five years old.
- Let [tex]\( x \)[/tex] be Charmaine's current age.
- The equation is: [tex]\( x + 14 = 25 \)[/tex].
- To find [tex]\( x \)[/tex], solve the equation:
[tex]\[
x + 14 = 25
\][/tex]
Subtract 14 from both sides:
[tex]\[
x = 11
\][/tex]
3. A number that is halved equals 4 more than 20.
- Let the number be [tex]\( y \)[/tex].
- The equation is: [tex]\( \frac{y}{2} = 20 + 4 \)[/tex].
- To find [tex]\( y \)[/tex], solve the equation:
[tex]\[
\frac{y}{2} = 24
\][/tex]
Multiply both sides by 2:
[tex]\[
y = 48
\][/tex]
4. A large pizza with 16 slices is shared among [tex]\( p \)[/tex] friends so that they can each have two slices.
- The equation is: [tex]\( \frac{16}{p} = 2 \)[/tex].
- To find [tex]\( p \)[/tex], solve the equation:
[tex]\[
\frac{16}{p} = 2
\][/tex]
Multiply both sides by [tex]\( p \)[/tex]:
[tex]\[
16 = 2p
\][/tex]
Divide by 2:
[tex]\[
p = 8
\][/tex]
5. Twenty-one, divided by the sum of a number and 5 equals 3.
- Let the number be [tex]\( z \)[/tex].
- The equation is: [tex]\( \frac{21}{z + 5} = 3 \)[/tex].
- To find [tex]\( z \)[/tex], solve the equation:
[tex]\[
\frac{21}{z + 5} = 3
\][/tex]
Multiply both sides by [tex]\( z + 5 \)[/tex]:
[tex]\[
21 = 3(z + 5)
\][/tex]
Divide by 3:
[tex]\[
z + 5 = 7
\][/tex]
Subtract 5 from both sides:
[tex]\[
z = 2
\][/tex]
6. A metre of rope costs R2.30. Peter wants to buy three and half metres.
- The cost of one metre of rope is R2.30.
- The number of metres Peter wants to buy is 3.5.
- The total cost is:
[tex]\[
\text{Total cost} = 2.30 \times 3.5 = 8.05
\][/tex]
So, the solutions to the problems are:
1. [tex]\( x = 5 \)[/tex]
2. Charmaine's current age [tex]\( x = 11 \)[/tex]
3. [tex]\( y = 48 \)[/tex]
4. [tex]\( p = 8 \)[/tex]
5. [tex]\( z = 2 \)[/tex]
6. Total cost of rope = R8.05
