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san4es73 [151]
3 years ago
9

Please help! just q4 and q5 thank you

Mathematics
1 answer:
Firdavs [7]3 years ago
3 0

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

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