Math Problem Statement

Translate the sentence into an equation: Four times the sum of a number and 3 equals 5. Use the variable c for the unknown number.

Solution

The problem asks you to translate the sentence into an equation:

"Four times the sum of a number and 3 equals 5."

Let the unknown number be cc. Here's how to break down the sentence:

  • "Four times the sum" means you need to multiply something by 4.
  • "The sum of a number and 3" refers to adding cc (the unknown number) and 3.
  • "Equals 5" means the result is equal to 5.

Now, putting all this together:

  • First, the sum of cc and 3 is (c+3)(c + 3).
  • Then, multiplying this sum by 4 gives 4(c+3)4(c + 3).
  • Finally, this is equal to 5, so the equation becomes:

4(c+3)=54(c + 3) = 5

This is the correct multi-step equation based on the problem's description.

Would you like more details or have any other questions?

Here are some related questions:

  1. How would you solve the equation 4(c+3)=54(c + 3) = 5 for cc?
  2. What happens if the number to be added was different, say 44 instead of 33?
  3. How would the equation change if it said "three times the sum" instead of "four times"?
  4. What if the sentence said "four times the product" instead of "four times the sum"?
  5. How can you check if your solution to cc is correct?

Tip: Always simplify expressions within parentheses first before multiplying or solving equations.

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Math Problem Analysis

Mathematical Concepts

Algebra
Linear Equations
Translating Sentences into Equations

Formulas

Multiplication of a sum: a(b + c)
Basic equation: ax + b = c

Theorems

Equality property of equations

Suitable Grade Level

Grades 6-8