Question

a family has \\$35 to spend on dinner. they spend \\$18 on entrees. side dishes are \\$3 each. what is the greatest number of side dishes they can buy?

6
4
5
7

Explanation:

Define the variable and constraints

Using the Writing Linear Inequalities and Real-world Inequality Constraints knowledge points
Let \(x\) represent the number of side dishes the family can buy.
The total budget is at most \(\$35\).
The cost of entrees is \(\$18\).
The cost of side dishes is \(\$3\) each.
The inequality representing this situation is:

$$18 + 3x \le 35$$

Solve the linear inequality

Using the Inequality Properties knowledge point
Subtract 18 from both sides:

$$3x \le 17$$

Divide both sides by 3:

$$x \le \frac{17}{3}$$

$$x \le 5.67$$

Determine the maximum discrete quantity

Using the Discrete Quantities knowledge point
Since the number of side dishes must be a whole number, we find the largest integer less than or equal to \(5.67\), which is \(5\).

Answer:

• 6
• 5 (Correct answer)
• 4
• 7