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

From this, we can express A in terms of B:

$a = \frac{2}{3}b$

This gives us:

$c = 0.75d$

Substituting $a$ and $c$ into the total weight equation:

$\frac{2}{3}b + b = 3(0.75d + d)$

This simplifies to:

$\frac{5}{3}b = 3(1.75d)$

From which we get:

$\frac{5}{3}b = 5.25d$

Expanding leads to:

$b = 3.15d$

Now substituting back to find $a$, $c$, and their ratios:

$a = \frac{2}{3}(3.15d) = 2.1d$ $c = 0.75d$

Thus we have:

$A : B : C : D = 2.1d : 3.15d : 0.75d : d$

Simplifying this ratio gives:

$A : B : C : D = 2.1 : 3.15 : 0.75 : 1$

To remove decimals, we multiply by 20:

$A : B : C : D = 42 : 63 : 15 : 20$