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Name Write and Solve an Inequality Beth wanted to go to the school dance but only had \( \$ 25 \) to spend. If the ticket cost \( \$ 5 \) how many cookies could Beth buy at the dance if each cookie costs \( \$ 1.25 \) ?

Ask by Elliott Edwards. in the United States
Nov 12,2024

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Beth can buy a maximum of 16 cookies.

Solución

To solve this problem, we need to set up an inequality based on the information given. Let's denote the number of cookies Beth can buy as \( x \). Given: - Beth has \( \$25 \) to spend. - The ticket cost is \( \$5 \). - Each cookie costs \( \$1.25 \). We can set up the inequality as follows: \[ 25 - 5 \geq 1.25x \] Now, we can solve this inequality to find the maximum number of cookies Beth can buy. Solve the inequality by following steps: - step0: Solve for \(x\): \(25-5\geq 1.25x\) - step1: Subtract the numbers: \(20\geq 1.25x\) - step2: Swap the sides: \(1.25x\leq 20\) - step3: Divide both sides: \(\frac{1.25x}{1.25}\leq \frac{20}{1.25}\) - step4: Divide the numbers: \(x\leq 16\) The solution to the inequality is \( x \leq 16 \). This means that Beth can buy a maximum of 16 cookies at the dance.

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The Deep Dive

To find out how many cookies Beth can buy, start by determining how much money she has left after buying the ticket. If the ticket costs \( \$ 5 \), then: \[ 25 - 5 = 20 \] Now, this means Beth has \( \$ 20 \) left to spend on cookies. The cost of each cookie is \( \$ 1.25 \). To find the maximum number of cookies she can buy, you set up the inequality: Let \( x \) be the number of cookies. Then: \[ 1.25x \leq 20 \] Solving for \( x \): \[ x \leq \frac{20}{1.25} \] \[ x \leq 16 \] So, Beth can buy a maximum of 16 cookies. Imagine this situationally: Beth, excited for the dance, has just enough for both the ticket and a mountain of cookies—all without breaking the bank! With 16 scrumptious treats in hand, she’s ready to dance the night away, fueled by her favorite sweet snack! In the midst of thoughtful budgeting and sweet menu choices, it's crucial to consider the overall experience. Making sure to enjoy the dance with friends while having snacks to share can turn a good evening into a great one! Balancing between ticket-purchasing and tasty treats not only keeps excitement alive but fosters camaraderie.

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