Charlie wants to order lunch for his friends. He'll order 6 sandwiches and a $2 kid's meal for his little brother. Charlie has $32. How much can he spend on each sandwich if they are all the same price?
Choose two answers: one for the inequality that models this situation and one for the correct answer.
A. Inequality: [tex]2 x+6 \leq 32[/tex]
B. Answer: $13 or less
C. Answer: $5 or less
D. Inequality: [tex]6 x+2 \leq 32[/tex]
E. Inequality: [tex]6 x+2 \geq 32[/tex]
F. Inequality: [tex]2 x+6\ \textless \ 32[/tex]
Answer (2)
Define the variable: Let x be the cost of each sandwich.
Formulate the inequality: 6 x + 2 ≤ 32 .
Solve for x : Subtract 2 from both sides to get 6 x ≤ 30 , then divide by 6 to find x ≤ 5 .
State the answer: Charlie can spend $5 or less on each sandwich.
Explanation
Problem Introduction Let's break down this problem step by step!
Setting up the Inequality First, we need to figure out how to represent the situation with an inequality. Let x be the cost of each sandwich. Charlie is buying 6 sandwiches, so the total cost for the sandwiches is 6 x . He also buys a kid's meal for $2 . The total amount he spends must be less than or equal to the amount of money he has, which is $32 . So, we can write the inequality as: 6 x + 2 ≤ 32
Solving the Inequality - Step 1 Now, let's solve the inequality to find the maximum amount Charlie can spend on each sandwich. We start by subtracting 2 from both sides of the inequality: 6 x + 2 − 2 ≤ 32 − 2 6 x ≤ 30
Solving the Inequality - Step 2 Next, we divide both sides by 6 to isolate x :
6 6 x ≤ 6 30 x ≤ 5
Finding the Answer This means Charlie can spend $5 or less on each sandwich.
Examples
Imagine you're planning a pizza party with friends. You have a budget and need to figure out how much you can spend on each pizza, considering delivery fees and drinks. This problem helps you set up an inequality to ensure you stay within your budget while maximizing the pizza fun!
Charlie can spend at most $5 on each sandwich. The inequality that models this situation is 6x + 2 ≤ 32. The two correct answers are D: Inequality: 6x + 2 ≤ 32 and C: Answer: $5 or less.
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