There are four boxes on a shelf, A, B, C and D - Edexcel - GCSE Maths - Question 17 - 2022 - Paper 3

From this statement, we have:

a = rac{2}{3}b

This leads to:

$c = 0.75d$

or equivalently, we can express it as:

c = rac{3}{4}d

Substituting $a$ and $c$ in terms of $b$ and $d$ into the first equation:

1. Substitute: $\frac{2}{3}b + b = 3\left(\frac{3}{4}d + d\right)$

2. Simplifying, we find: $\frac{5}{3}b = 3\left(\frac{7}{4}d\right)$ $\frac{5}{3}b = \frac{21}{4}d$

3. Thus, by rearranging, $b = \frac{21}{4} \cdot \frac{3}{5} d = \frac{63}{20}d$

4. Now substituting back to find $a$ and $c$: $a = \frac{2}{3} \cdot b = \frac{2}{3} \cdot \frac{63}{20}d = \frac{42}{20}d$ $c = \frac{3}{4}d$

Now we have:

• $a = \frac{42}{20}d$
• $b = \frac{63}{20}d$
• $c = \frac{3}{4}d = \frac{15}{20}d$
• $d = d$

Thus the ratios become:

$a : b : c : d = \frac{42}{20} : \frac{63}{20} : \frac{15}{20} : 1$

Or after eliminating $d$: $42 : 63 : 15 : 20$