/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 20 The tallest snowman ever recorde... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 3: Problem 20

The tallest snowman ever recordedreally a snow woman named Olympia-was built by residents of Bethel, Maine, and surrounding towns. Her body and head together made up her total record height of 122 ft. The body was \(2 \mathrm{ft}\) longer than 14 times the height of the head. What were the separate heights of Olympia's head and body?

Short Answer

Expert verified
The head is 8 feet, and the body is 114 feet.

Step by step solution

01

- Define Variables

Let's denote the height of Olympia's head as \(h\) feet. The height of the body will be represented as \(b\) feet.
02

- Set Up the Equations

From the problem statement, we have two key pieces of information:1. The total height of Olympia is 122 feet.2. The body is 2 feet longer than 14 times the height of the head.This gives us the following equations:\[h + b = 122\] and \[b = 14h + 2\]
03

- Substitute the Second Equation into the First

Substitute \(b\) from the second equation into the first equation:\[h + (14h + 2) = 122\]Simplify this to:\[15h + 2 = 122\]
04

- Solve for h

Subtract 2 from both sides to isolate the terms with \(h\):\[15h = 120\]Divide by 15:\[h = 8\]
05

- Solve for b

Use the value of \(h\) to find \(b\):\[b = 14h + 2\]Substitute \(h\) with 8:\[b = 14(8) + 2 = 112 + 2 = 114\]
06

- Verify the Solution

Finally, verify the values by checking the total height:\[h + b = 8 + 114 = 122\]The calculations are correct, confirming the separate heights.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Linear equations
Linear equations are foundational in algebra. They are equations where the highest power of the variable is one. That means you'll often see them written in the form: ax + b = cTo solve them, you usually isolate the variable on one side of the equation. For instance, in our snowperson problem, we used the information given to form two linear equations:
By solving these linear equations step-by-step, we can find the height of Olympia鈥檚 head and body. Understanding how linear equations function is crucial for dealing with algebra word problems effectively.
Variable substitution
Variable substitution is a method to solve systems of equations. It involves replacing one variable with an expression from another equation. This is exactly what was done in the snowperson problem. Here's a quick refresher:
  • Step 1: Write both equations clearly:
    • h + b = 122
    • b = 14h + 2
  • Step 2: Substitute the expression for b () into the first equation:
    • h + (14h + 2) = 122
After substitution, you have a simpler equation with just one variable to solve. This makes it easier to find the values of both variables involved. This technique is essential for solving many algebraic equations.
Problem-solving strategies
Good problem-solving strategies are key to tackling algebra word problems. Here are some strategies we used for this problem:
  • Define variables: Identify and define what each variable represents. Here, we defined the height of the head as 'h' and the body as 'b'.
  • Write equations: Translate the word problem into algebraic equations. In our example, we had:
    • h + b = 122
    • b = 14h + 2
  • Substitute and solve: Use substitution to solve the system of equations.
  • Verify your solution: Always check your results to ensure accuracy. For its problem, we verified that the total height matched.
Using these strategies not only simplifies problem-solving but also helps in understanding the logical flow of algebraic operations.
Height calculation
Height calculation is a common requirement in problem-solving. It's essential to understand how to work with units and relationships between different parts of a structure. Here, we were dealing with the heights of Olympia's head and body.First, we defined our variables and used the given relationships between those heights. Then, we substituted and solved the equations. Remember the steps:
  • Identify all the given information
  • Set up equations based on that information
  • Substitute values and solve
  • Verify your results to ensure calculations are correct
Practicing different height-related problems can make these steps more intuitive and strengthen your algebra skills overall.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

The ACT is a standardized test for students entering college. Each of the four scores that a student receives has a benchmark value. Students scoring at or above the benchmarks are considered ready to succeed in college. The benchmark for the science test is 6 points higher than the benchmark for the English test. The sum of the reading and mathematics benchmarks is 1 point more than the sum of the English and science benchmarks. The sum of the English, mathematics, and science benchmarks is 1 point more than three times the reading benchmark. The sum of all four benchmarks is \(85 .\) Find all four benchmarks.

Automotive Maintenance. The radiator in Natalie's car contains \(6.3 \mathrm{L}\) of antifreeze and water. This mixture is \(30 \%\) antifreeze. How much of this mixture should she drain and replace with pure antifreeze so that there will be a mixture of \(50 \%\) antifreeze?

Nutrition. Most nutritionists now agree that a healthy adult diet includes \(25-35\) g of fiber each day. A breakfast of 2 bran muffins, 1 banana, and a 1-cup serving of Wheaties contains 9 g of fiber; a breakfast of 1 bran muffin, 2 bananas, and a 1 -cup serving of Wheaties contains 10.5 g of fiber; and a breakfast of 2 bran muffins and a 1 -cup serving of Wheaties contains \(6 \mathrm{g}\) of fiber. How much fiber is in each of these foods? Data: usda.gov and InteliHealth.com

Find the slope of the graph of \(f(x)=8 .\) If the slope is undefined, state this. [ 2.4]

Students in a Listening Responses class bought 40 tickets for a piano concert. The number of tickets purchased for seats in either the first mezzanine or the main floor was the same as the number purchased for seats in the second mezzanine. First mezzanine seats cost 52 dollars each, main floor seats cost 38 dollars each, and second mezzanine seats cost 28 dollars each. The total cost of the tickets was 1432 dollars. How many of each type of ticket were purchased?
See all solutions

Recommended explanations on Math Textbooks

Mechanics Maths

Read Explanation

Probability and Statistics

Read Explanation

Decision Maths

Read Explanation

Logic and Functions

Read Explanation

Applied Mathematics

Read Explanation

Calculus

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.