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John wants to buy flowers for his grandma. Roses cost [tex]$3 each, and carnations cost $[/tex]2 each. John has a budget of $35.
1. Write an inequality that represents this situation. 2. If John buys 8 carnations, what is the maximum number of roses he can buy?
1. Define the costs and budget: - The cost of one rose is [tex]$3.
- The cost of one carnation is $[/tex]2. - John's total budget is [tex]$35.
2. Formulate the inequality:
Let \( r \) represent the number of roses and \( c \) represent the number of carnations. The total amount John spends on roses and carnations must be less than or equal to his budget. This can be represented by the inequality:
\[
3r + 2c \leq 35
\]
3. Calculate the cost of the 8 carnations John buys:
John buys 8 carnations, so we calculate the total cost of carnations:
\[
\text{Cost of 8 carnations} = 8 \times 2 = 16 \text{ dollars}
\]
4. Determine the remaining budget after buying carnations:
Subtract the amount spent on carnations from the total budget:
\[
\text{Remaining budget} = 35 - 16 = 19 \text{ dollars}
\]
5. Calculate the maximum number of roses John can buy with the remaining budget:
Since each rose costs $[/tex]3, we divide the remaining budget by the cost of one rose: [tex]\[
\text{Maximum number of roses} = \left\lfloor \frac{19}{3} \right\rfloor = 6 \text{ roses}
\][/tex]
Thus, after buying 8 carnations, John can buy a maximum of 6 roses with the remaining budget.
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