Question

1. john wants to buy flowers for his grandma. roses cost $3 each. carnations cost $2 each. john has a budget of $35. write an inequality that represents this situation. if john buys 8 carnations, what is the maximum number of roses he can buy?

Explanation:

Step1: Define variables

Let \( r \) be the number of roses and \( c \) be the number of carnations. The cost of roses is \( 3r \) dollars and the cost of carnations is \( 2c \) dollars. The total cost must be less than or equal to the budget of \( 35 \) dollars. So the inequality is \( 3r + 2c \leq 35 \).

Step2: Substitute \( c = 8 \)

We know \( c = 8 \), so substitute into the inequality: \( 3r + 2(8) \leq 35 \).

Step3: Simplify the inequality

First, calculate \( 2(8)=16 \), so the inequality becomes \( 3r + 16 \leq 35 \). Then subtract \( 16 \) from both sides: \( 3r \leq 35 - 16 \), which simplifies to \( 3r \leq 19 \).

Step4: Solve for \( r \)

Divide both sides by \( 3 \): \( r \leq \frac{19}{3} \approx 6.33 \). Since the number of roses must be an integer, the maximum number of roses is \( 6 \).

Answer:

The inequality is \( 3r + 2c \leq 35 \), and the maximum number of roses John can buy when he buys 8 carnations is \( 6 \).