Math Problem Statement

In a group of 5 friends =, the average height is 153 cm. Ken is 148 cm tall, Maria is 145 cm, and Marcus is 162 cm. The other two are the same height how tall are they?

Solution

We are given that the average height of 5 friends is 153 cm. This means the total height of all five friends is:

Total height=153×5=765 cm\text{Total height} = 153 \times 5 = 765 \text{ cm}

We also know the heights of three friends:

  • Ken = 148 cm
  • Maria = 145 cm
  • Marcus = 162 cm

The sum of their heights is:

148+145+162=455 cm148 + 145 + 162 = 455 \text{ cm}

Let the height of each of the remaining two friends be x cm. Since they have the same height, their total contribution is:

2x2x

Now, we set up the equation:

455+2x=765455 + 2x = 765

Solving for xx:

2x=7654552x = 765 - 455

2x=3102x = 310

x=155x = 155

Thus, the two remaining friends are 155 cm tall each.

Would you like a step-by-step breakdown for clarity? Here are some related questions to explore:

  1. What happens to the average height if a new person of 160 cm joins the group?
  2. How would the answer change if one of the remaining two friends was 157 cm instead?
  3. Can you find the median height of the group after solving for the missing values?
  4. How would the average change if Marcus were replaced with someone 10 cm shorter?
  5. How do you calculate the range of the given heights?

Tip: When solving for an unknown in an average problem, always start by finding the total sum using the given average!

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Math Problem Analysis

Mathematical Concepts

Averages
Algebra
Linear Equations

Formulas

Average formula: (Sum of values) / (Number of values) = Average
Equation setup: Total height = Sum of known heights + 2x

Theorems

Basic average theorem

Suitable Grade Level

Grades 6-8