4 Steps to Math Problem Solving

Summary

This video tutorial demonstrates how to solve two math word problems: determining hourly wages and calculating the dimensions of a rectangular room. The first problem shows how to find Adam and Isabelle's hourly wages by dividing their total weekly earnings by hours worked, then comparing their rates. The second problem focuses on finding the length and width of a room using its perimeter and a relationship between its length and width. The video emphasizes the importance of planning, solving, and checking your work to ensure accuracy in problem-solving.

Takeaways

• 📊 Isabelle worked 20 hours last week and earned $145.80, while Adam worked 15 hours and earned $112.50.
• 🕒 The goal is to find out how much each person earns per hour by dividing their total earnings by the number of hours worked.
• 💸 Isabelle earns $7.29 per hour, and Adam earns $7.50 per hour.
• 📉 To determine how much more Adam earns per hour than Isabelle, subtract Isabelle's hourly wage from Adam's.
• 💵 Adam earns $0.21 more per hour than Isabelle.
• 📝 Always check your work by reviewing the problem and verifying the calculations.
• 📐 The second problem involves a rectangular room, where the length is one inch more than three times the width, and the perimeter is 26 inches.
• 🧮 The formula for perimeter is 2 times the length plus 2 times the width.
• 🔢 The width is represented as X, and the length is 3X + 1.
• 📏 After solving, the width is 3 inches and the length is 10 inches.
• ✅ The solution is verified by plugging the dimensions back into the perimeter formula to confirm the result is 26 inches.

Q & A

Question 1: How much did Isabelle and Adam earn in total last week?

Isabelle earned $145.80, and Adam earned $112.50 last week.

Question 2: What is the goal when comparing Isabelle’s and Adam’s earnings?

The goal is to determine how much each earns per hour and how much more Adam earns per hour compared to Isabelle.

Question 3: How can you calculate Isabelle’s and Adam’s hourly earnings?

To calculate their hourly earnings, divide the total amount earned by the number of hours worked. For Isabelle, divide $145.80 by 20 hours. For Adam, divide $112.50 by 15 hours.

Question 4: How much does Isabelle earn per hour?

Isabelle earns $7.29 per hour.

Question 5: How much does Adam earn per hour?

Adam earns $7.50 per hour.

Question 6: How much more does Adam earn per hour than Isabelle?

Adam earns $0.21 more per hour than Isabelle.

Question 7: What is the formula for calculating the perimeter of a rectangular room?

The formula for the perimeter is 2 times the length plus 2 times the width (P = 2L + 2W).

Question 8: How is the length of the room related to the width?

The length is one inch more than three times the width, or L = 3W + 1.

Question 9: How do you find the dimensions of the room given the perimeter?

You set up an equation using the perimeter formula, substitute the expressions for length and width, solve for the width, and then use that value to find the length.

Question 10: What are the final dimensions of the room?

The width is 3 inches, and the length is 10 inches.

Outlines

00:00

💰 Calculating Hourly Wages for Isabelle and Adam

The paragraph discusses how Isabelle and Adam worked different hours and earned different weekly salaries. Isabelle worked 20 hours and earned $145.80, while Adam worked 15 hours and earned $112.50. The task is to find out how much each earned per hour and compare their hourly wages. The problem-solving process includes reading the problem, paraphrasing it, planning a solution, and solving the calculations. Isabelle earns $7.29 per hour, and Adam earns $7.50 per hour. After subtracting Isabelle's hourly rate from Adam's, it is found that Adam earns $0.21 more per hour. Finally, the paragraph emphasizes checking the work by reviewing the problem and verifying calculations to ensure the solution is correct.

05:01

📏 Solving a Perimeter Problem for a Rectangular Room

This paragraph explains how to find the dimensions of a rectangular room using a word problem. The given information includes that the room's length is one inch more than three times the width, and the perimeter is 26 inches. The formula for the perimeter is stated as 2 times the length plus 2 times the width. The width is represented as 'X,' and the length as '3X + 1.' By substituting these expressions into the perimeter formula, the paragraph explains the step-by-step process of solving for X. The width is found to be 3 inches, and the length is calculated as 10 inches. It highlights the importance of drawing diagrams and checking the work by substituting the dimensions back into the perimeter formula to confirm the solution is accurate. The paragraph ends by encouraging readers to feel confident in solving similar word problems.

Keywords

💡Hourly wage

Hourly wage refers to the amount of money a person earns for each hour of work. In the video, Isabelle earns $7.29 per hour, while Adam earns $7.50 per hour. The task involves calculating how much more Adam makes per hour compared to Isabelle, emphasizing the importance of knowing their hourly rates.

💡Total earnings

Total earnings represent the overall amount of money earned in a given period, such as a week. In this context, Isabelle earned $145.80 for working 20 hours, and Adam earned $112.50 for working 15 hours. The video uses these figures to help determine their hourly wages.

💡Perimeter

Perimeter is the total length of the boundaries of a shape, such as a rectangle. In the video, the perimeter of a rectangular room is given as 26 inches. The video demonstrates how to use this information, along with the relationship between the room’s length and width, to calculate the room’s dimensions.

💡Length

Length refers to the longest side of a rectangle. The video describes a room where the length is one inch more than three times the width. This relationship is crucial for solving the problem of finding the room's dimensions when its perimeter is given.

💡Width

Width is the shorter side of a rectangle. In the video, the width is represented by 'X', and the length is expressed as a function of the width. This helps to set up the equation needed to solve for both the width and the length using the perimeter formula.

💡Equation

An equation is a mathematical statement that shows the equality of two expressions. The video uses an equation to represent the relationship between the perimeter of the room and the dimensions of its length and width. Solving this equation helps to determine the room's dimensions.

💡Solution plan

A solution plan refers to the strategy used to solve a problem step by step. In the video, the narrator emphasizes planning a solution before solving word problems, which includes understanding the question, using formulas, and checking calculations to ensure the solution is correct.

💡Distributive property

The distributive property is a mathematical principle that allows you to multiply a single term by each term in a sum or difference inside parentheses. In the video, this property is used when expanding the formula for the perimeter to help solve for the room's dimensions.

💡Check your work

Checking your work involves reviewing the problem and solution to ensure accuracy. The video stresses the importance of rereading the problem, verifying calculations, and confirming that the solution answers the original question. This step ensures that errors are identified and corrected.

💡Word problem

A word problem is a mathematical problem presented in a narrative format. The video provides examples of word problems, such as calculating hourly wages or determining room dimensions based on the perimeter. Solving word problems requires translating the narrative into mathematical equations and finding the solution.

Highlights

Isabelle worked 20 hours last week and earned $145.80, while Adam worked 15 hours and earned $112.50.

The problem requires finding out how much each person earns per hour.

The strategy is to divide the total amount earned by the number of hours worked for each person.

Isabelle makes $7.29 per hour, and Adam makes $7.50 per hour.

To find out how much more Adam earns per hour, subtract Isabelle's hourly rate from Adam's hourly rate.

Adam earns $0.21 more per hour than Isabelle.

It's crucial to check the calculations to ensure there were no errors.

Understanding the problem involves determining the hourly wages given their weekly earnings and hours.

The next problem involves a rectangular room where the length is one inch more than three times the width.

The goal is to find the room’s dimensions given a perimeter of 26 inches.

Start by setting up an equation for the perimeter using the length and width.

Let the width be represented as 'X' and the length as '3X + 1'.

Plug these values into the formula for the perimeter and solve for X.

The width is 3 inches, and the length is 10 inches.

Checking the result shows that the calculated dimensions match the given perimeter, confirming the solution is correct.

Transcripts

Isabelle worked 20 hours last week and

earned 145 dollars and 80 cents Adam

worked 15 hours last week and earned one

hundred and twelve dollars and fifty

cents how much more does Adam earn per

hour

okay so step one is reading and

paraphrasing which just means putting it

in your own words we know how much

Isabel makes in a week and we know how

much Adam makes in a week what we don't

know is how much they make per hour so

that's what we have to find out our next

step is to plan a solution we know how

much they made per week but we don't

know how much they made per hour to find

this if we take the total amount they

made per week and divide it by the

number of hours they worked to find a

difference in our early salaries we

would subtract the two amounts now we

have to solve we can see that Isabel

makes seven dollars and twenty-nine

cents per hour and Adam makes seven

dollars and fifty cents per hour to find

out how much more Adam makes we would

take Adams hourly salary subtract

Isabel's hourly salary and you get 21

cents and lasts most importantly we have

to check our work we want to make sure

that we reread the problem and we really

understand what the question is that's

being asked you want to check your

calculations and make sure that you

didn't make any silly errors as you can

see we got our problem correct great job

in the blueprints of a rectangular room

the length is one inch more than three

times the width find the dimensions if

the perimeter is 26 inches the first

step is to understand the question they

give us the perimeter and we need to

find the length and the width the

formula for a perimeter is two times the

length plus two times the width or an

expanded form length plus length plus

width plus width now it's time to plan

our solution we know the length is one

more than three times the width so we're

going to call the width X and we're

going to call the length three X plus

one after that we're going to plug those

two less statements into the formula for

the perimeter another important step in

solution planning is using pictures or

diagrams whenever possible in this

specific example we're talking about a

rectangular room which makes it easy for

us to draw a rectangle and label the

sides we label the sides with L and W

and fill in the left statements now we

have to solve plug the let statements

into the perimeter formula the first

thing you do is distribute by

multiplying

next you combine like terms that are on

the right-hand side then subtract two

from each side they get X by itself and

finally divide by eight and you get that

X is three one more step we did find X

but we need to find the length and the

width so we have to plug X back into the

length and the width formula the width

is X so the width is three inches the

length is three X plus one so the length

when we plug in X is going to be 10

inches and last but certainly not least

we have to check our work we know the

width is three and the length is 10 they

gave us that the perimeter is 26 and

this is how we can check our work plug

the length from the width into the

perimeter formula and see if it equals

26 and it does so we know we have the

right answer

you

hopefully this tutorial built your

confidence in solving any type of word

problem you did a great job thanks for

watching