Given that \[ \frac{a}{b} = \frac{2}{5} \] and \[ \frac{b}{c} = \frac{3}{4} \] find \( a:b:c \) - Edexcel - GCSE Maths - Question 11 - 2020 - Paper 1

From the second equation, ( \frac{b}{c} = \frac{3}{4} ), we can express ( b ) in terms of ( c ):

[ b = \frac{3}{4}c ]

We now substitute the expression for ( b ) into the expression for ( a ):

[ a = \frac{2}{5}\left(\frac{3}{4}c\right) = \frac{6}{20}c = \frac{3}{10}c ]

Now we can express ( a, b, c ) in terms of ( c ):

• ( a = \frac{3}{10}c )
• ( b = \frac{3}{4}c )

To find the ratio ( a:b:c ), we can express all terms with a common denominator:

• ( a = \frac{3}{10}c = \frac{3}{10}\cdot \frac{4}{4} = \frac{12}{40}c )
• ( b = \frac{3}{4}c = \frac{3}{4}\cdot \frac{10}{10} = \frac{30}{40}c )
• ( c = 1c = \frac{40}{40}c )

Thus, the ratio ( a:b:c ) can be expressed as:

[ a:b:c = 12:30:40]

To simplify further, we can divide all terms by 2:

[ a:b:c = 6:15:20]