Q41. - Algebra 1

Question

Write an equation and solve each problem.

Moving lava can build up and form beaches at the coast of an island. The growth of an island in a seaward direction may be modeled as $8y+2$ centimeters, where $y$ represents the number of years that the lava flows. An island has expanded 60 centimeters seaward. How long has the lava flowed?

Step-by-Step Solution

Answer

The lava has flowed for $7\frac{1}{4}$ years or equivalently 7 years 3 months.

Step 1. List the given data.

The growth of an island in a seaward direction is $8y+2$ centimeters where $y$ represents the number of years that the lave flows.

 

An island has expanded 60 centimeters seaward.

Step 2. Write the equation for the given problem.

Translating the given problem into equation form,

 

$8y+2=60$

 

This is the required equation for the given problem.

Step 3. Solve the equation.

Solving,

 

$8y+2=60$  (Obtained equation)

 

$8y+2-2=60-2$  (Subtract 2 from both sides)

 

$8y=58$  (Simplify)

 

$\frac{8y}{8}=\frac{58}{8}$  (Divide both sides by 8)

 

$y=7\frac{1}{4}$  (Simplify)

 

So, $y=7\frac{1}{4}$ is the solution of the obtained equation.

Step 4. Interpret the obtained solution.

According to the assumption, $y$ is the number of years that the lava flowed.

 

Thus, the lava has flowed for $7\frac{1}{4}$ years or equivalently 7 years 3 months.