Math Problem Statement

Maggie has a $50 gift card that she will use to purchase games for her phone. Each game costs $1.99. She has a coupon code for $5 off her entire purchase. Which equation can be used to find x, the maximum number of games Maggie can purchase? A 50 = 1.99 − 5x B 50 = 1.99 + 5x C 50 = 1.99x + 5 D 50 = 1.99x − 5

Solution

We need to set up an equation that accounts for Maggie’s total spending, including the price of the games and the discount.

  • Maggie starts with a $50 gift card.
  • Each game costs $1.99.
  • She also has a $5 coupon that applies to the entire purchase.

Let's define x as the number of games Maggie can purchase.

The total cost of the games would be 1.99x (since each game costs $1.99). After applying the $5 coupon, the total amount Maggie pays is 1.99x - 5.

Since she can spend up to $50, we set the total cost equal to $50:

1.99x5=501.99x - 5 = 50

This matches option D:

D:50=1.99x5\boxed{D: 50 = 1.99x - 5}

So, option D is the correct equation.

Would you like more details on solving this equation, or do you have any other questions? Here are some related questions:

  1. How do you solve the equation 50=1.99x550 = 1.99x - 5 for xx?
  2. How would the equation change if Maggie didn’t have the $5 coupon?
  3. What if Maggie had $60 on the gift card instead of $50? How would the equation change?
  4. What is the total cost of 10 games after applying the $5 coupon?
  5. What is the maximum number of games Maggie can buy if the coupon was worth $10 instead?

Tip: Always break down word problems into known values (like the price per game, gift card amount, and coupon) before translating them into an equation.

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Math Problem Analysis

Mathematical Concepts

Algebra
Linear Equations

Formulas

1.99x - 5 = 50

Theorems

Linear equation solving

Suitable Grade Level

Grades 7-9