All the solutions provided in McGraw Hill My Math Grade 5 Answer Key PDF Chapter 11 Lesson 3 Problem-Solving Investigation: Use Logical Reasoning will give you a clear idea of the concepts.
McGraw-Hill My Math Grade 5 Answer Key Chapter 11 Lesson 3 Problem-Solving Investigation: Use Logical Reasoning
Learn the Strategy
Three friends each measured their height Their heights are 4 feet 10 inches, 4 feet 9 inches, and 4 feet 7 inches. Use the clues to determine the height in inches, of each person.
- Elliot is taller than Jorge.
- Nicole is 3 inches taller than the shortest person.
- Elliot is 57 inches tall.
1. Understand
What facts do you know?
the clues that are listed above
What do you need to find?
the ___________ of each person
Answer: We need to find out the height of each person
2. Plan
I can use logical reasoning to find the height of each person.
3. Solve
Convert the measurements to inches to compare.
4 × 12 + 10 = 48 + 10 = ___________ inches
Nicole is _____________ inches tall.
4 × 12 + 9 = 48 + 9 = _____________ inches
Elliot is _____________ inches tall.
4 × 12 + 7 = 48 + 7 = _____________ inches
Jorge is _____________ inches tall.
Answer:
4 × 12 + 10 = 48 + 10 = 58 inches
Nicole is 58 inches tall.
4 × 12 + 9 = 48 + 9 = 57 inches
Elliot is 57 inches tall.
4 × 12 + 7 = 48 + 7 = 55 inches.
Jorge is 55 inches tall.
4. Check
Is my answer reasonable?
Since all of the answers match the clues, the solution is reasonable.
Answer: yes, all the answers are reasonable.
The answers we got and the above-given conditions were all matches.
Hence, our answer is reasonable.
Practice the Strategy
Three dogs are sitting in a line. Rocky is not last. Coco is in front of the tallest dog. Marley is sitting directly behind Rocky. List the dogs in order from first to last.
1. Understand
What facts do you know?
What do you need to find?
answer:
Rocky is not last
Coco is in front of the tallest dog
Marley is behind rocky
We need to find out the order of the dogs from first to last.
2. Plan
Answer:
We can use logical reasoning to find out the order of the dogs. Make a table to help organize the information.
3. Solve
Answer:
Place ‘x’ in each box that cannot be true.
Rocky cannot be last.
Coco cannot be last since he is in front of another dog.
Marley is behind, so Marley cannot be first.
Therefore, the order is Coco, Rocky and Marley.
4. Check
Is my answer reasonable?
Answer: yes
since all the answers match the above-given clues.
Hence, the answer is reasonable.
Apply the Strategy
Solve each problem by using logical reasoning.
Question 1.
An after-school club is building a clubhouse that has a rectangular floor that is 8 feet by 6 feet. What is the total floor area, in square inches, of the clubhouse?
Answer:
Before finding the solution to the problem given, we need to know the area of a rectangle formula.
The area of the rectangle = length x width
First, convert feet to inches:
1 foot is equal to 12 inches:
1ft = 12″
The distance d in inches (″) is equal to the distance d in feet (ft) times 12:
d(“) = d(ft) x 12
The above-given feet: 8 and 6
d(“) = 8 x 12 = 96
d(“) = 6 x 12 = 72
Now multiply both the inches:
The total floor area = 96 x 72
The total floor area is 6912 square inches.
Question 2.
There is a red, green, and yellow bulletin board hanging in the hallway. All of the bulletin boards are rectangular with a height of 4 feet. Their lengths are 6 feet, 5 feet, and 3 feet. The red bulletin board has the largest area and the yellow one has the smallest area. What is the area of the green bulletin board?
Answer:
The above-given:
There are three colour bulletin board hangings. The colours are red, green, and yellow.
1. The facts we know are:
All the bulletin boards are the same height at 4 feet.
The given lengths are 6 feet, 5 feet, and 3 feet.
The bulletin colour board has the largest area is red
The bulletin colour board has the smallest area is yellow.
We need to find out the area of the green bulletin board.
2. Plan:
We can use the area of the rectangle formula to find out the area. Make a table to help organize the information.
3. solve:
The area of the rectangle = length x height
The red colour board is having larger area compared to green and yellow.
The yellow colour board is having smaller area compared to red and green.
The remaining green colour board is having 20 square feet.
Therefore, the area of the green colour bulletin board is 20 square feet.
Question 3.
Mathematical PRACTICE Look for a Pattern If the pattern below continues, how many pennies will be in the fifth figure?
Answer:
By observing figures 1, 2 and 3 we made figures 4 and 5.
In figure 1, there is one penny
In figure 2, there is 1 + 2 = 3 pennies
In figure 3, there are 1 + 2+ 3 = 6 pennies.
In figure 4, there are 1 + 2 + 3 + 4 = 10 pennies
In figure 5, there are 1 + 2+ 3 + 4 + 5 = 15 pennies.
Therefore, 15 pennies are there in the fifth figure.
Question 4.
A cafeteria table has an area of 21 square feet. If three tables are pushed together, what is the combined area of the tables?
Answer:
The above-given:
The area of the cafeteria table = 21
The number of tables pushed together = 3
The combined area of the tables = T(A)
T(A) = 21 x 3
T(A) = 63
Therefore, the combined area of the tables is 63 square feet.
Question 5.
Ethan has $1.25 in dimes, nickels, and pennies. He has twice as many dimes as pennies, and the number of nickels is one less than the number of pennies. How many dimes, nickels, and pennies does he have?
Answer:
Assume that he has ‘x’ pennies
The number of dimes he has is: 2x
The number of nickels he has is: x – 1
the total money he has is 2x(0.1) + (x – 1)(0.050 + x (0.01)
need to memorize that: 1 dime = $0.1; 1 nickel = $0.05; 1 penny = $0.01
Now solve the equation:
2x(0.1) + (x – 1)(0.050 + x (0.01) = 1.25
0.2x + 0.05x – 0.05 + 0.01x = 1.25
0.26x = 1.25 + 0.05
0.26x = 1.3
x = 1.3 / 0.26
x = 5
Now substitute x value.
2x = 2 x 5 = 10
Therefore, he has 10 dimes.
x – 1 = 5 – 1 = 4
He has 4 nickels.
we got x = 5
Therefore, he has 5 pennies.
Finally, 10 dimes; 4 nickels; 5 pennies.
Review the Strategies
Use any strategy to solve each problem.
- Use logical reasoning.
- Draw a diagram.
- Look for a pattern.
- Solve a simpler problem.
Question 6.
Madeline has 2 times the number of games as Paulo. Paulo has 4 more games than Tyler. If Tyler has 9 games, how many games are there among the 3 friends?
Answer:
The above-given:
Madeline = 2p
Paulo = 4 + T
T = 9
Now we know the Tyler games. So we can easily find out about the Paulo games.
The number of Paulo games = 4 + T = 4 + 9 = 13
We got Paulo’s number of games. Now we can easily calculate Madeline games.
The number of Madeline games = 2p = 2 x 13 = 26
The number of games among three friends = 9 + 13 + 26 = 48.
Therefore, 48 games among three friends.
Question 7.
When Cheryl goes mountain climbing, she rests 5 minutes for every 15 minutes that she climbs. If Cheryl’s combined time is 2 hours, how many minutes does she rest?
Answer:
For every 15 minutes – she takes 15 minutes of rest
For 2 hours – The number of minutes she takes rest.
1 hour = 60 minutes
2 hours = 2 x 60 = 120 minutes.
Therefore, for 2 hours she takes 40 minutes of rest.
Question 8.
There are 8 girls for every 7 boys on a field trip. If there are 56 girls on the trip, how many students are on the trip?
Answer:
Let ‘x’ represents the number of boys.
According to the above-given information, the equation is:
8 / 7 = 56 / x
Now solve the equation:
8x = 56 * 7
8x = 392
x = 392 / 8
x = 49
Now we know the count of girls and boys.
The total number of girls = 56
The total number of boys = 49
Now add both values to get a total number of students.
The total number of students = 56 + 49 = 105.
Therefore, a total of 105 on a trip.
Question 9.
There are 4 more girls in Mrs Pitt’s class than Mr Brown’s class. Five girls moved from Mrs Pitt’s class to Mr Brown’s class. Now there are twice as many girls in Mr Brown’s class as there are in Mrs Pitt’s. How many girls were in Mr Brown’s class, to begin with?
Answer: 7 girls
Explanation:
Assume that there are x girls in Mr Brown’s class, to begin with.
So, the equation would be: x + 5 = 2(x – 1)
x + 5 = 2x – 2
x – 2x = -2 – 5
-x = -7
‘-‘ gets cancelled
x = 7
Therefore, there are 7 girls in Mr brown’s class, to begin.
Question 10.
A storage room measures 48 inches by 60 inches. What is the total area, in square feet, of the closet?
Answer:
We need to find out the area.
The above-given inches are 48 and 60
Area of the rectangle = length x width
Area = 48 x 60
Area = 2880
Therefore, the area of the closet is 2,880 square feet.
Question 11.
Mathematical PRACTICE Make Sense of Problems Five friends go to a batting cage. Andrea bats after Daniel and before Jessica. Juwan bats after Andrea and before Jessica and Filipe. Jessica always bats immediately after Juwan. Who bats last?
Answer:
There are 5 friends. They are Daniel, Andrea, Jessica, Juwan, and Flippe.
Facts:
Daniel – Andrea – Jessica
Andrea – Juwan – Jessica and Flippe
Juwan – Jessica
Plan: use logical thinking for better understanding we can make a table.
solve:
Keep ‘x’ that is not true.
The first is Daniel
The second is Andrea
The third is Juwan
The fourth is Jessica and the last is Flippe.
Therefore, the last bat is Flippe.
McGraw Hill My Math Grade 5 Chapter 11 Lesson 3 My Homework Answer Key
Problem Solving
Solve each problem by using logical reasoning.
Question 1.
Mathematical PRACTICE Use Math Tools Mr Toshi’s fifth-grade class sold containers of popcorn and peanuts. If each day they sold 25 fewer containers of peanuts than popcorn, how many containers of popcorn and peanuts did they sell in all? Complete the table and solve.
Answer:
The main key point is 25 fewer containers of peanuts.
The peanuts in day 1 is 225 – 25 = 200
The peanuts in day 2 is 200 – 25 = 175
The peanuts on day 3 are 150 – 25 = 125
The peanuts on day 4 are 300 – 25 = 275
The popcorn and peanuts on day 1 = 225 + 200 = 425
The popcorn and peanuts on day 2 = 200 + 175 = 375
The popcorn and peanuts on day 3 = 150 + 125 = 275
The popcorn and peanuts on day 4 = 300 + 275 = 575
The number of many containers of popcorn and peanuts they sell in all = x
x = 425 + 375 + 275 + 575
x = 1650
Therefore, 1650 containers of popcorn and peanuts.
Question 2.
A shelter house has a floor area of 400 square feet. If three identical shelter houses are built, what is the combined floor area of the shelter houses?
Answer:
The above-given:
The area of the shelter house = 400 sqft
If three identical shelter houses are built then the combined area of the shelter house. Let it be A.
A = 400 x 3 Or we can add (400 + 400 + 400)
A = 1200 sqft
Therefore, the area of the shelter house after a combined three houses is 1200 square feet.
Question 3.
Meghan has $1.10 in dimes, nickels, and pennies. She has three times as many nickels as pennies, and the number of dimes is two less than the number of pennies. How many dimes, nickels, and pennies does she have?
Answer:
We have 1 dime = 10 cents
1 nickel = 5 cents
1 penny = 1 cent
Let’s say x dime; y nickels; z pennies.
10x + 5y + z = 110
y = 3z
x = z – 2
10(z – 2) + 5(3z) + z = 110
10z – 20 + 15z + z = 110
26z – 20 = 110
26z = 130
z = 130/26
z = 5
Now substitute the z value
y = 3z = 3(5) = 15
x = z – 2 = 5 – 2 = 3
pennies = 5; nickels = 15; dimes = 3
Question 4.
Alana is 4 years older than her brother Ernie. Ernie is 2 years older than their sister Amelia. Amelia is 10 years younger than their brother Mazo. If Mazo is 17 years old, how old is Alana?
Answer:
The above-given:
Mazo = 17 years
Amelia = 17 – 10 = 7 years
Erine = 2 + A = 2 + 7 = 9 years
Alaria = 4 + E = 4 + 9 = 13 years
Finally, Alana is 13 years old.
Question 5.
A rectangular garden measures 15 feet by 30 feet. What is the total area, in square yards, of the garden?
Answer:
The above-given feet: 15 and 30
We need to convert feet to yards:
1 yard is equal to 3 feet:
1yd = 3ft
The distance d in yards (yd) is equal to the distance d in feet (ft) divided by 3:
d(yd) = d(ft) / 3
length in yards = 30 / 3 = 10
width in yards = 15 / 3 = 5
The area = 10 x 5
The area = 50
Therefore, the area of the garden is 50 square yards.