4 Steps to Math Problem Solving
Summary
TLDRThis 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
💰 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.
📏 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.
Mindmap
Keywords
💡Hourly wage
💡Total earnings
💡Perimeter
💡Length
💡Width
💡Equation
💡Solution plan
💡Distributive property
💡Check your work
💡Word problem
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
関連動画をさらに表示
More Word Problems Using Quadratic Equations - Example 1
SOLVING PROBLEMS INVOLVING QUADRATIC EQUATIONS || GRADE 9 MATHEMATICS Q1
62. A Norman window has the shape of a rectangle surmounted by a semicircle. If the perimeter of...
MATH 6 QUARTER 1 WEEK 6 | MUTI-STEP PROBLEM INVOLVING WHOLE NUMBERS AND DECIMALS
Solving Problems Involving Quadratic Equations and Rational Algebraic Equations (Part 1)
Solving Addition Math Problems | Elementary Math
5.0 / 5 (0 votes)