A number is added to both the numerator and the denominator of the fraction \(\frac{1}{8}\) if the result is \(\frac{1}{2}\), find the number.

Gifty, Justina, and Frank shared 60 oranges in the ratio 5: 3: 7 respectively. How many oranges did Justina receive?

Find the quadratic equation whose roots are \(\frac{2}{3}\) and - 1

A piece of rod of length 44 m is cut to form a rectangular shape such that the ratio of the length to the breadth is 7: 4. Find the breath.

In the diagram above, \(\overline{MN} || \overline{KL}\), \(\overline{ML}\) and \(\overline{KN}\) intersect at X. |\(\overline{MN}\)| = 12cm, |\(\overline{MX}\)| = 10cm and |\(\overline{MN}\)| = 9cm. If the area of \(\triangle\) MXN is 16cm\(^2\), calculate the area of \(\triangle\) LXK