All the solutions provided in **McGraw Hill Math Grade 5 Answer Key PDF Chapter 10 Lesson 12 Problem-Solving Investigation: Draw a Diagram** will give you a clear idea of the concepts.

## McGraw-Hill My Math Grade 5 Answer Key Chapter 10 Lesson 12 Problem-Solving Investigation: Draw a Diagram

**Learn the Strategy**

Jaheim visited an aquarium over the weekend and saw 35 species of fish. This was \(\frac{1}{5}\) the total number of species of fish. How many total species of fish are at the aquarium?

1. Understand

What facts do you know?

Jaheim saw ____ species of fish, which is _____ of the total number of species.

What do you need to find?

• the total number of species of ____ in the aquarium

Answer:

By reading the question, we get to know some hints.

The facts we know:

The number of species of fish Jaheim saw = 35

The amount of the total number of species = 1/5

We need to find out the total number of species of fish in the aquarium.

2. Plan

I can solve the problem by drawing a diagram.

Answer:

We can draw a model to represent the total number of species in the aquarium.

– A bar model can be defined as a pictorial representation of a number in the form of bars or boxes used to solve number problems. Bar models help us to attain an understanding of how a problem needs to be solved and calculated.

– Bar models help us to understand what operations, whether addition, subtraction, multiplication or/and division should be used to solve a word problem.

Each box represents 35.

so, the 35 x 5 = 175

3. Solve

The model is divided into fifths. Since each part represents 35 species, there is a total of 35 × 5, or ____ species of fish at the aquarium.

Answer:

The model is divided into fifths

each box represents 35

to find out the total numbers of species of fishes we need to multiply.

so, 35 x 5 = 175

Therefore, the total number of species of fishes are 175.

4. Check

Is my answer reasonable? ____ ÷ 5 = 35

Answer:

To check whether the answers are reasonable or not we need to divide

175 ÷ 5 = 35

Therefore, the answer is reasonable.

**Practice the Strategy**

Victor has $18 in a piggy bank. He spends \(\frac{2}{3}\) of the money on a video game and \(\frac{1}{6}\) on candy. How much money will Victor have left?

1. Understand

What facts do you know?

____________________

____________________

What do you need to find?

____________________

Answer:

Above-given facts:

The total money Victor has in the piggy bank = $18

The amount he spends on video games = 2/3

The amount he spends on candy = 1/6

After spending all the amount of money we need to find out the amount he left.

2. Plan

____________________

Answer:

We can solve the problem by using the diagram.

By using the bar model we can solve.

We can draw a model to represent the total number of species in the aquarium.

– A bar model can be defined as a pictorial representation of a number in the form of bars or boxes used to solve number problems. Bar models help us to attain an understanding of how a problem needs to be solved and calculated.

– Bar models help us to understand what operations, whether addition, subtraction, multiplication or/and division should be used to solve a word problem.

3. Solve

Answer:

The above-given:

2/3 and 1/6

add these two

2/3 + 1/6 (take LCM as 6)

4 + 1/6 = 5/6

Now we need to calculate 5/6 of 18

The total amount Victor spend = 5/6

Now divide the bar diagram into six equal parts. There would be $3 in each section.

Therefore, Victor has $3 left.

4. Check

Is my answer reasonable? Explain.

____________________

Answer:

To check whether the answer is reasonable or not. we need to divide and check

18 ÷ 6 = 3

Therefore, the answer is reasonable.

**Apply the Strategy**

**Solve each problem by drawing a diagram.**

Question 1.

Mrs Vallez purchased sand toys that were originally $20. She received \(\frac{1}{4}\) off of the total price. How much did she save?

Answer:

The above-given:

The original amount of sand toys purchased by Vallez = 20

The amount she received = 1/4

The amount she saves = X

We can solve the problem by using the diagram

Now we have to divide the bar diagram into four equal parts.

In each section, we have to write 5.

Therefore, she saves $5.

To check whether the answer is reasonable or not.

20 ÷ 5 = 4

Therefore, the answer is reasonable.

Question 2.

Sue has four DVDs and Terry has six DVDs. They put all their DVDs together and sold them for $10 for two DVDs. How much money will they earn if they sell all of their DVDs?

Answer:

The above-given

The number of DVDs Sue has = 4

The number of DVDs Terry has = 6

The total number of DVDs they have together = 6 + 4 = 10

The money they want to earn = X

X = 10/2 x 10

X = 5 x 10

X = 50

Therefore, they will earn $50 if they sell all of their DVDs.

Question 3.

**Mathematical PRACTICE 4 Model Math** Jacinda is decorating cookies for a class party. She can decorate \(\frac{2}{3}\) of a cookie per minute. At this rate, how many cookies can she decorate in 15 minutes?

Answer:

The above-given

The time she can decorate a cookie per minute = 2/3

The number of cookies she can decorate in 15 minutes = C

for 1 minute – 2/3 of the cookie

for 15 minutes – how many cookies? (C)

C x 1 = 15 x 2/3

C = 30/3

C = 10

Therefore, she can decorate 10 cookies within 15 minutes.

Question 4.

At a bird sanctuary, Ricky counted 80 birds. Of the birds he counted, \(\frac{1}{4}\) were baby birds.

If he counted an equal number of adult males r and females, how many adult female birds did Ricky count?

Answer:

The number of birds counted by Ricky = 80

Out of 80 birds, the number of baby birds = 1/4

We can write in mathematical form as:

1/4 of 80

We need to find out the number of adult female birds.

from the above-given conditions, we have to calculate

1/4 x 80 = 20

The total number of baby birds = 20

Now subtract the total number of birds and a total number of baby birds. Let it be A.

A = 80 – 20

A = 60

Now we got the adult birds (female and male).

Here we have to find out about the female birds. Let it be F

F = 60/2

F = 30

Therefore, the number of female birds is 30.

And finally, we can summarize that the baby birds are 20; female birds are 30; male birds are 30.

Question 5.

**Mathematical PRACTICE 5 Use Math Tools** To make chocolate ice cream, you need about \(\frac{3}{8}\) pound of chocolate. How many pounds of chocolate will you need to make 4 batches of ice cream?

Answer:

The amount of chocolate we need to make a chocolate Ice-cream = 3/8

The number of pounds of chocolate we need to make 4 batches of ice cream = C

C = 3/8 x 4

C = 12/8

C = 3/2

Therefore, 3/2 pounds of chocolate is needed.

**Review the Strategies**

Use any strategy to solve each problem.

- Draw d diagram.
- Work backwards.
- Guess, check, and revise.
- Act it out.

Question 6.

A cook needs 12 pounds of flour. He wants to spend the least amount of money. If a 2-pound bag costs $1.59 and a 5-pound bag costs $2.89, how many bags of each type of flour should he buy? What will be the total cost?

Answer:

The pounds of flour a cook needs = 12

The cost of a 2-pound bag is $1.59

The cost of a 5-pound bag is $2.89

we can buy two 5-pound bags and one 2-pound bag

The total cost can be:

2.89 x 2 = 5.78 (the total cost of 5-pound bags)

1.59 x 1 = 1.59 (the total cost of 2-pound bags)

Now add both the costs.

The total cost of both bags = 5.78 + 1.59 = 7.37.

Therefore, the total cost is $7.37

Question 7.

**Mathematical PRACTICE 5 Use Math Tools** A ride at a theme park lasts 1\(\frac{1}{2}\) minutes. It takes 2 minutes to prepare the ride for each trip. How many times can the ride be completed in 30 minutes?

Answer:

The minutes to last a ride at a theme park = 1 1/2 = 3/2 = 1.5 minutes

The number of minutes will take to prepare the ride for each trip = 2

The number of rides we can complete in 30 minutes = M

The total time = 2 + 1.5 = 3.5

If one ride requires 3.5 minutes, the number of rides that can be completed in 30 minutes

M = 30/3.5

M = 8.57

M = 8

Therefore, within 30 minutes, 8 times a ride can be completed.

Question 8.

On Monday, 21 DVDs were checked out at the library. This is 3 less than half the amount of books checked out that day. How many books were checked out?

Answer:

The number of DVDs was checked on Monday = 21

half of the amount of books = 1/2b

The equation can be written as:

DVDs = 1/2b – 3

21 = 1/2b – 3

21 + 3 = 1/2b

24 = 1/2b (24 = b/2)

b = 2 x 24

b = 48

Therefore, the number of books checked out is 48.

Question 9.

**Mathematical PRACTICE 4 Model Math** Leo takes 30 minutes to eat dinner, 15 minutes to change clothes, and 20 minutes to walk to practice. If Leo needs to be at hockey practice at 7:15 P.M., what time does he need to begin?

Answer:

The time it takes Leo to eat dinner = 30 min

The time it takes Leo to change clothes is 15 min

The time it takes Leo to walk is 20 min

Add all the minutes: 30 + 15 + 20 = 65 minutes.

He needs to begin 1 hour 5 minutes before from 7:15 PM

He needs to begin at 6:10 PM

Question 10.

Mi-Ling sets up tables for her art class students. Each square table can seat two people on each side. How many people can be seated if 8 square tables are pushed together in a row?

Answer:

The number of people who can seat at a square table on each side = 2

The number of people who can be seated at 8 square tables = X

Therefore, at 8 square table 36 people can be seated.

### McGraw Hill My Math Grade 5 Chapter 10 Lesson 12 My Homework Answer Key

**Problem Solving**

**Solve each problem by drawing a diagram.**

Question 1.

Paul is decorating cupcakes for a birthday party. He can decorate \(\frac{3}{4}\) of a cupcake per minute. At this rate, how many cupcakes can he decorate in 12 minutes?

Answer:

The time is taken by paul to decorate 3/4 of a cupcake = 1 min

The number of cupcakes he can decorate in 12 minutes = C

for 3/4 th – 1 min

for C – 12 min

C x 1 = 3/4 x 12

C = 3 x 3

C = 9

Therefore, he can decorate 9 cupcakes in 12 minutes.

Question 2.

**Mathematical PRACTICE 4 Model Math** To make cheesecake, you need about 2\(\frac{1}{2}\) pounds of cream cheese. How many pounds of cream cheese will you need to make 2 cheesecakes?

Answer:

The number of pounds of cream needed to make cheesecake = 2 1/2 = 5/2 pounds

The number of pounds of cream cheese to make 2 cheesecakes = C

5/2 pounds – 1 cake

C – 2 cakes

C x 1 = 5/2 x 2

C = 5

Therefore, 5 pounds of cream cheese is needed.

Question 3.

Scott viewed 72 classic cars at a car show. Of the cars he viewed, \(\frac{3}{8}\) were sports cars. How many sports cars did Scott view?

Answer:

The number of classic cars viewed by Scott = 72

The number of cars he viewed sport cars = 3/8

The number of sports = 3/8 x 72

The number of sports cars = 3 x 9 = 27

Therefore, he viewed 27 sports cars.

Question 4.

**Mathematical PRACTICE 5 Use Math Tools** A builder is installing a fence on all four sides of a backyard. The

yard is 40 feet long and 50 feet wide. How much fencing will the builder need?

Answer:

The number of feet for long = 40

The number of feet for wide = 50

for two sides = 40 + 40 = 80 (long)

for two sides = 50 + 50 = 100 (wide)

The builder needs = 80 + 100 = 180 feet.

Question 5.

Misty purchased a pair of jeans that were originally $24 but was on sale for \(\frac{1}{3}\) off of the total price. How much did she save?

Answer:

The original amount of jeans Misty has purchased = 24

The offer = 1/3 of total price

1/3 of 24

1/3 x 24

1 x 8 = 8

Therefore, the amount she saved is $8.