Question #dfbed

Dec 24, 2016

So, the dog will eat $\left(7 + \frac{7 d}{3}\right)$ cans in $\left(3 + d\right)$ days.

Explanation:

Let $x$ be the number of cans that can be eaten by it in $\left(3 + d\right)$ days.

Here the ratio number of cans $= 7 : x$

The ratio of number of days $= 3 : \left(3 + d\right)$

Here the number of cans and days are in direct proportion.

$\therefore 7 : x = 3 : \left(3 + d\right)$

or, $\frac{7}{x} = \frac{3}{3 + d}$

or, $3 x = 7 \left(3 + d\right) \rightarrow$ Cross multiply.

or, $3 x = 21 + 7 d$

or, $\frac{3 x}{3} = \frac{21 + 7 d}{3} \rightarrow$ Dividng both sides by 3.

or, $x = \frac{21}{3} + \frac{7 d}{3} \rightarrow$ Split RHS

or, $x = 7 + \frac{7 d}{3}$

So, the dog will eat $\left(7 + \frac{7 d}{3}\right)$ cans in $\left(3 + d\right)$ days.