Math Problem Statement
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: .
- 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 = .
- 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 = .
- 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: .
- 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:
- What happens if Kami spends $10 on transportation instead of $5 per day?
- How can we calculate a raise if it was a 5% instead of 4% for Donnie?
- How would you calculate the new gas price if the drop was 15% instead of 19%?
- What if the coupon discount at the pizza shop was 15% instead of 10%? How would the expression change?
- 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
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