Question

A certain tiger shark is 55 cm long at birth and grows 2.5 cm / year. A certain hammerhead shark is 25 cm long at birth and grows 5 cm/year. When will the sharks be equal in length? Let x = time in years Let y = length of the sea creatures

Answer 1

A certain tiger shark is 55 cm long at birth and grows 2.5 cm / year.

So we will add 55 to (2.5 multiplied by the number of years) to get the length of the tiger shark. Since x = time in years, we have

`\begin{gathered} 55+2.5* x=y \\ 55+2.5x=y \\ y=55+2.5x \end{gathered}`

Hence, the equation for the length of the tiger shark is

`y=55+2.5x`

We wiil do same process to get the equation for the hammerhead shark

The hammerhead shark grows 25cm at birth and grows 5 cm/year.

So the equation will be

`\begin{gathered} 25+5* x=y \\ 25+5x=y \\ y=25+5x \end{gathered}`

Hence the equation for the length of the spinny hammerhead shark is

`y=25+5x`

Solving both equations simultaneously we have

`\begin{gathered} y=55+2.5x \\ y=25+5x\text{ (multiplying this by minus sign we have) } \\ -y=-25-5x \\ \text{Paring with the first equation and eliminating y, we have } \\ y=55+2.5x \\ -y=-25-5x \\ 0=30-2.5x \\ 2.5x=30 \\ x=(30)/(2.5) \\ x=12 \end{gathered}`

Since x = 12, hence, the sharks will be equal in length in 12 years