A & B share the cost in a ratio of 7:2. A pays £126, how...

The sum of the parts of the ratio ${\displaystyle =7+2=9}$
Of which A pays 7 of the parts and B, 2 of the parts.
Since A pays 7 parts then 1 part ${\displaystyle =₤126÷7=\pounds 18}$
Hence 2 parts ${\displaystyle =2\times \pounds 18=\pounds 36}$
Thus B pays £36
As a check: Total paid ${\displaystyle =\pounds 126+\pounds 36=\pounds 162}$
and ${\displaystyle \pounds 162÷9=\pounds 18}$
Answer: ₤ 36

B pays £36.00
Explanation:
Using ratio in the format of a fraction.
$\frac{\text{Payment by A}}{\text{Payment by B}}=\frac{7}{2}=\frac{\pounds 126}{B}$
Turning it upside down (makes it easier to determine B)
${\displaystyle \frac{2}{7}=\frac{B}{126}}$
Multiply both sides by 126
${\displaystyle \frac{2}{7}\times 126=\frac{B}{126}126}$
${\displaystyle \frac{252}{7}=B\times \frac{126}{126}}$
But ${\displaystyle \frac{126}{126}=1\text{so}B\times 1=B}$ giving:
${\displaystyle B=\frac{252}{7}=36}$
B pays £36.00