Math Problem Statement

After a math contest, Basil noticed that there were four extra-large pizzas that were left untouched. In addition, another three slices of pizza were uneaten. If there were a total of 51 slices of pizza left, how many slices does an extra-large pizza have? Herman and Jacquita are saving money for college. Herman currently has $15,000 and is working hard to save $1,000 per month. Jacquita has only $12,000 but is saving $1,300 per month. In how many months will they have the same amount of savings? George bought some CDs at his local store for $15.95 each. Nora bought the same number of CDs from a store online for $13.95 each, plus an $8 shipping fee. In the end, both George and Nora spent the same amount of money buying their CDs. How many CDs did George buy?

Solution

Let's go over the questions shown in the image:

  1. Question 7: After a math contest, Basil noticed that four extra-large pizzas were left untouched. In addition, three slices were uneaten. If there were a total of 51 slices of pizza left, how many slices does each extra-large pizza have?

    • The equation given is 4x+3=514x + 3 = 51, where xx represents the number of slices in one extra-large pizza.
  2. Question 8: Herman and Jacquita are saving money for college. Herman currently has $15,000 and is saving $1,000 per month. Jacquita has $12,000 but is saving $1,300 per month. In how many months will they have the same amount of savings?

    • You need to set up an equation for both savings and solve for the number of months.
  3. Question 9: George bought some CDs at a store for $15.95 each. Nora bought the same number of CDs from an online store at $13.95 per CD, plus an additional $8 for shipping. Both George and Nora spent the same amount in total. How many CDs did George buy?

    • You need to set up an equation based on total costs for both and solve for the number of CDs.

Would you like to proceed with the solutions to these questions, or do you need more clarification on any specific one?

Also, here are 5 related questions to practice:

  1. How do you solve an equation with two variables like in the second problem?
  2. How do you set up equations when comparing two people's savings strategies?
  3. What is the general strategy for solving word problems involving costs and quantities?
  4. How can linear equations help solve practical financial planning problems?
  5. How do you verify your solutions in such algebraic problems?

Tip: Always define the variables before writing an equation—it helps in keeping track of what you're solving for.

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Math Problem Analysis

Mathematical Concepts

Linear Equations
Simultaneous Equations
Word Problems

Formulas

Linear equation: ax + b = c
Simultaneous equations: Set equal expressions for two variables and solve

Theorems

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Suitable Grade Level

Grades 8-10