Math Problem Statement

The user provided an image containing a puzzle with four mathematical problems. The user is required to match each problem with the correct expression from three given options, forming a code.

Solution

Let's go through each problem and match the correct expression.

Problem 1: Kami has $200 and spends $12 per day on food and $5 per day on transportation.

  • Total spending per day = $12 (food) + $5 (transportation) = $17 per day.
  • Thus, Kami's remaining amount after d days is: 20017d200 - 17d.
  • Correct Option: A (200 – 17d).

Problem 2: Donnie earns $12 an hour. He got a 4% raise and now earns $12.48. Write an expression to show how his new hourly rate was calculated.

  • New hourly rate = Original hourly rate + 4% increase = 12×1.0412 \times 1.04.
  • Correct Option: C (12 × 1.04).

Problem 3: Gas prices dropped 19% overnight. Write an expression that represents the new price of gas using (g) as the old price.

  • New gas price = Original price - 19% of the original price = g0.19g=0.81gg - 0.19g = 0.81g.
  • Correct Option: A (0.81g).

Problem 4: You have a $2 off coupon you can use at the Pizza Shop as well as a 10% coupon you can use after the $2. Write an expression that would represent how much you pay before tax using (p) as the original price of the pizza.

  • First, subtract $2, then apply a 10% discount: 0.9(p2)0.9(p - 2).
  • Correct Option: B (0.9(p - 2)).

Final Code:

  • The correct options are A, C, A, B, so the code is: ACAB.

Would you like a detailed explanation of any part of this?

Here are 5 related questions to further explore:

  1. What happens if Kami spends $10 on transportation instead of $5 per day?
  2. How can we calculate a raise if it was a 5% instead of 4% for Donnie?
  3. How would you calculate the new gas price if the drop was 15% instead of 19%?
  4. What if the coupon discount at the pizza shop was 15% instead of 10%? How would the expression change?
  5. Can you derive a formula for Kami's budget if she has an additional fixed weekly expense?

Tip: Always verify your expressions by plugging in example numbers to check if the results make sense!

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Math Problem Analysis

Mathematical Concepts

Linear Equations
Percentage Calculations
Discounts
Algebraic Expressions

Formulas

Linear formula for remaining balance: 200 - 17d
Percentage increase formula: New value = Old value × (1 + Percentage)
Percentage decrease formula: New value = Old value × (1 - Percentage)
Expression for combining a fixed coupon and percentage discount: 0.9(p - 2)

Theorems

Basic principles of percentage increase and decrease
Algebraic manipulation of expressions

Suitable Grade Level

Grades 6-8