Mathematics 4024 · O Level · Equations

Equations — practice question

Bag $A$ has red balls and green balls. Altogether, the bag contains $x$ balls. The number of green balls is $6$ greater than the number of red balls.
(a)[2]

Show that the fraction of the balls in bag $A$ that are red is $\frac{x-6}{2x}$.

(b)[2]

Bag $B$ also has red balls and green balls. The number of red balls in bag $B$ is $x$. The number of green balls in bag $B$ is $4$ times the number of green balls in bag $A$. Show that the fraction of the balls in bag $B$ that are red is $\frac{x}{3x+12}$.

(c)[3]

From $\frac{x-6}{2x} = \frac{x}{3x+12}$, Show that $x^2 - 6x - 72 = 0$.

(d)[2]

Solve by factorisation the equation $x^2 - 6x - 72 = 0$.

(e)[1]

$x$ gives the total number of balls in bag $A$. Use your answer to part (d) to find how many green balls are in bag $A$.

Worked solution & mark scheme

This 10-mark question has a full step-by-step worked solution and mark scheme. One marking point: $\frac{x-6}{2x}$

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