Question

Eric is on diet where he must eat between 1500 and 3000 calories per day.If he already had 750 calories for breakfast, how many can he have the rest of the day?Variable Represents:Inequality:Solve.Sentence:

Answer 1

Eric has a limit of calories of:

$1500\leq\text{Eric}\leq300$

The value of calories Eric eats in that day is given by:

$\text{Eric}=x+750$

Where "x" is the value of the calories he can still eat. The inequality is:

$1500\leq x+750\leq3000$

To solve it we need to break it into two inequalities.

$\begin{gathered} x+750\leq3000 \\ x+750\ge1500 \end{gathered}$

We need to solve them individually.

$\begin{gathered} x+750\leq3000 \\ x\leq3000-750 \\ x\leq2250 \end{gathered}$$\begin{gathered} x+750\ge1500 \\ x\ge1500-750 \\ x\ge750 \end{gathered}$

The result is:

$750\leq x\leq2250$

Eric can eat between 750 and 2250 calories on that day.