19
2019

Question 3
(Marks: 15)
Q.3.1 If , what is the value of ?
(4)
Q.3.2 If p and q are integers such that , then what is the value of ?
(3)
Q.3.3 Simplify
(2)
Q.3.4 Lebo bought oranges for R8 each and Thato bought apples for R12 each. In total, they
(6) paid R104 for 10 fruits.

How many apples did Thato buy?

Question 4
(Marks: 15)
Q.4.1

Solve the inequality . Show all steps.
(5)

Ask by Wagner Schultz. in South Africa

Mar 26,2025

Question

19
2019

Question 3
(Marks: 15)
Q.3.1 If , what is the value of ?
(4)
Q.3.2 If p and q are integers such that , then what is the value of ?
(3)
Q.3.3 Simplify
(2)
Q.3.4 Lebo bought oranges for R8 each and Thato bought apples for R12 each. In total, they
(6) paid R104 for 10 fruits.

How many apples did Thato buy?

Question 4
(Marks: 15)
Q.4.1

Solve the inequality . Show all steps.
(5)

Ask by Wagner Schultz. in South Africa

Mar 26,2025

UpStudy AI · Accepted Answer

### Q.3.1 Solve the equation: $$ 3^{n-2}+2^{2}=13 $$ Since $$2^2=4$$, the equation becomes: $$ 3^{n-2}+4=13 $$ Subtract $$4$$ from both sides: $$ 3^{n-2}=9 $$ Recognize that $$9=3^2$$, thus: $$ 3^{n-2}=3^2 $$ So, the exponents must be equal: $$ n-2=2 \quad \Longrightarrow \quad n=4 $$ --- ### Q.3.2 We are given that $$p$$ and $$q$$ are integers such that: $$ p+q=9 $$ We need to find the value of: $$ \frac{q-9}{4p} $$ Express $$q$$ in terms of $$p$$: $$ q=9-p $$ Substitute into the expression: $$ \frac{(9-p)-9}{4p}=\frac{-p}{4p} $$ Cancel $$p$$ (assuming $$p\neq 0$$): $$ -\frac{1}{4} $$ --- ### Q.3.3 Simplify the expression: $$ 60-30\div3\times5+7 $$ Follow the order of operations (division and multiplication first): $$ 30\div3=10 \quad \text{and} \quad 10\times5=50 $$ The expression becomes: $$ 60-50+7 $$ Perform the subtraction and addition: $$ 60-50=10 \quad \Longrightarrow \quad 10+7=17 $$ --- ### Q.3.4 Let the number of oranges be $$O$$ and the number of apples be $$A$$. We have: $$ \text{Total fruits: } O+A=10 $$ Lebo bought oranges at R8 each and Thato bought apples at R12 each, and the total cost is R104: $$ 8O+12A=104 $$ Express $$O$$ in terms of $$A$$: $$ O=10-A $$ Substitute into the cost equation: $$ 8(10-A)+12A=104 $$ Simplify: $$ 80-8A+12A=104 \quad \Longrightarrow \quad 80+4A=104 $$ Subtract $$80$$ from both sides: $$ 4A=24 \quad \Longrightarrow \quad A=6 $$ Thus, Thato bought $$6$$ apples. --- ### Q.4.1 Solve the inequality: $$ \frac{15}{2}-x>\frac{37}{4} $$ **Step 1:** Subtract $$\frac{15}{2}$$ from both sides: $$ -x>\frac{37}{4}-\frac{15}{2} $$ **Step 2:** Express $$\frac{15}{2}$$ with a denominator of $$4$$: $$ \frac{15}{2}=\frac{30}{4} $$ Now the inequality becomes: $$ -x>\frac{37-30}{4}=\frac{7}{4} $$ **Step 3:** Multiply both sides by $$-1$$. Remember to reverse the inequality sign: $$ x<-\frac{7}{4} $$ ### Q.3.1 $$ n = 4 $$ --- ### Q.3.2 $$ \frac{q-9}{4p} = -\frac{1}{4} $$ --- ### Q.3.3 $$ 17 $$ --- ### Q.3.4 Thato bought $$6$$ apples. --- ### Q.4.1 $$ x < -\frac{7}{4} $$

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