Question

Rodney is helping to make hamburgers for the football game. He's made 10 hamburgers so far. His coach asked him to make at least 30 hamburgers but no more than 80. Solve the inequality and interpret the solution.

Answer 1

Given that:

Rodney is helping to make hamburgers for the football game. He's made 10 hamburgers so far.

His coach asked him to make at least 30 hamburgers but, no more than 80.

The inequality is

`30\leq a+10\leq80`

Solving the inequalities separately;

For the first part

`\begin{gathered} 30\leq a+10 \\ Collect\text{ like terms} \\ 30-10\leq a \\ 20\leq a \end{gathered}`

For the other part;

`\begin{gathered} a+10\leq80 \\ Collect\text{ like terms} \\ a\leq80-10 \\ a\leq70 \end{gathered}`

The solution to the inequality is

`20\leq a\leq70`

From the solution;

Hence, we can conclude that Rodney must make at least 20 more hamburgers but, not more than 70 hamburgers.