Total for Question 4: 12 marks

5. (a) Find the value of [tex]x[/tex].
(i) [tex]\frac{x}{5} = \frac{4}{3}[/tex]

(ii) [tex]\frac{3}{x} = \frac{2}{5}[/tex]

(iii) [tex]\frac{4}{5} = \frac{x}{\frac{1}{2}}[/tex]



Answer :

Sure! Let's solve each part of this question step-by-step.

### (a) Finding the value of [tex]\( x \)[/tex].

(i) [tex]\( x:5 = 4:3 \)[/tex]

To solve this, we can set up a proportion:
[tex]\[ \frac{x}{5} = \frac{4}{3} \][/tex]

Now, we use cross multiplication to find [tex]\( x \)[/tex]:
[tex]\[ x \cdot 3 = 4 \cdot 5 \][/tex]

So,
[tex]\[ 3x = 20 \][/tex]

Finally, we solve for [tex]\( x \)[/tex] by dividing both sides by 3:
[tex]\[ x = \frac{20}{3} = 6.666666666666666 \][/tex]

So, the value of [tex]\( x \)[/tex] in part (i) is:
[tex]\[ x = 6.666666666666666 \][/tex]

(ii) [tex]\( 3:x = 2:5 \)[/tex]

Set up the proportion:
[tex]\[ \frac{3}{x} = \frac{2}{5} \][/tex]

Using cross multiplication:
[tex]\[ 3 \cdot 5 = 2 \cdot x \][/tex]

So,
[tex]\[ 15 = 2x \][/tex]

Solving for [tex]\( x \)[/tex] by dividing both sides by 2:
[tex]\[ x = \frac{15}{2} = 7.5 \][/tex]

Thus, the value of [tex]\( x \)[/tex] in part (ii) is:
[tex]\[ x = 7.5 \][/tex]

(iii) [tex]\( 4:5 = x:\frac{1}{2} \)[/tex]

Set up the proportion:
[tex]\[ \frac{4}{5} = \frac{x}{\frac{1}{2}} \][/tex]

Using cross multiplication:
[tex]\[ 4 \cdot \frac{1}{2} = 5 \cdot x \][/tex]

Which simplifies to:
[tex]\[ 2 = 5x \][/tex]

Solving for [tex]\( x \)[/tex]:
[tex]\[ x = \frac{2}{5} = 0.4 \][/tex]

Therefore, the value of [tex]\( x \)[/tex] in part (iii) is:
[tex]\[ x = 0.4 \][/tex]

### Summary of Results:
- For (i) [tex]\( x = 6.666666666666666 \)[/tex]
- For (ii) [tex]\( x = 7.5 \)[/tex]
- For (iii) [tex]\( x = 0.4 \)[/tex]