Math Problem Statement

Paula, Bobby and Charlie shared a box of sweets. Bobby received twice as many sweets as Paula. Charlie received thrice as many sweets as Bobby. If Charlie received 165 more sweets than Paula, how many sweets did Charlie receive?

Solution

Let's define the variables to represent the number of sweets each person received:

  • Let PP represent the number of sweets Paula received.
  • Bobby received twice as many sweets as Paula, so Bobby received 2P2P sweets.
  • Charlie received thrice as many sweets as Bobby, so Charlie received 3×2P=6P3 \times 2P = 6P sweets.

We are told that Charlie received 165 more sweets than Paula. This can be written as: 6P=P+1656P = P + 165

Now, let's solve this equation step by step:

  1. Subtract PP from both sides: 6PP=1656P - P = 165 5P=1655P = 165

  2. Divide both sides by 5: P=1655=33P = \frac{165}{5} = 33

Now that we know Paula received 33 sweets, we can calculate how many sweets Charlie received: 6P=6×33=1986P = 6 \times 33 = 198

Therefore, Charlie received 198 sweets.

Would you like further explanation or details on the problem? Here are some related questions:

  1. How many sweets did Bobby receive?
  2. How many sweets did Paula receive?
  3. What was the total number of sweets shared among Paula, Bobby, and Charlie?
  4. If Charlie had received 10 more sweets, how many would he have received in total?
  5. What is the ratio of sweets received by Paula, Bobby, and Charlie?

Tip: Always start by defining variables and building relationships based on the problem statement when solving word problems.

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Math Problem Analysis

Mathematical Concepts

Algebra
Linear Equations

Formulas

6P = P + 165
5P = 165
P = 33
6P = 198

Theorems

Basic Algebraic Manipulation
Proportional Relationships

Suitable Grade Level

Grades 6-8