Question

In a certain country, the consumption of tea is five times the consumptions of coffee. If $a$ percent more tea and $b$ percent more coffee was consumed, the aggregate amount consumed would be $7c$ per cent. more; but if $b$ per cent. more tea and $a$ percent more coffee were consumed, the aggregate amount consumed would be $3c$ percent more ,compare $a$ and $b$.

Answer 1

Let $x$ be the consumption of coffee and $5x$ be the consumption of tea. Then total consumption will be $6x$.

Then according to the question,

$5x\frac{a}{100}+x\frac{b}{100}=6x\frac{7c}{100}\to 5a+b=42$

$5x\frac{b}{100}+x\frac{a}{100}=6x\frac{3c}{100}\to 5b+a=18$

Dividing both the equations,

$\frac{5a+b}{5b+a}=\frac{42}{18}=\frac{7}{3}$

$15a+3b=35b+7a$

$8a=32b$

$a=4b$