Question

Please help! just q4 and q5 thank you

Answer 1

First exercise

Given

$\dfrac{3x+1}{x+4}=\dfrac{2}{3}$

We can cross multiply this equation to get

$3(3x+1)=2(x+4)$

Expand both terms:

$9x+3=2x+8$

Subtract 2x from both sides:

$7x+3=8$

Subtract 3 from both sides:

$7x=5$

Divide both sides by 7:

$x=\dfrac{5}{7}$

Second exercise

Let $p,o,a$ be the number of pine, oath and ash trees. We are given:

$\begin{cases}\frac{p}{o} = \frac{5}{8} \iff p = \frac{5o}{8}\\\frac{o}{a} = \frac{2}{3} \iff o=\frac{2a}{3}\\p+o+a=300\end{cases}$

We can substitute the expression for p of the first equation in the last equation to get

$p+o+a=300\iff \dfrac{5o}{8}+o+a=300 \iff \dfrac{13}{8}o+a=300$

Now we use the second equation, to express o in terms of a:

$\dfrac{13}{8}o+a=300 \iff \dfrac{13}{8}\cdot \dfrac{2}{3}a+a=300 \iff \dfrac{25}{12}a = 300 \iff a = 300\cdot \dfrac{12}{25} = 144$