## Engage NY Eureka Math 5th Grade Module 4 Lesson 24 Answer Key

### Eureka Math Grade 5 Module 4 Lesson 24 Problem Set Answer Key

Question 1.

A vial contains 20 mL of medicine. If each dose is \(\frac{1}{8}\) of the vial, how many mL is each dose? Express your answer as a decimal.

Answer:

Each dose has a 2.5 ml dose.

Explanation:

Here, a vial contains 20 mL of medicine, and if each dose is \(\frac{1}{8}\) of the vial, so each dose has \(\frac{1}{8}\) × 20 ml which is \(\frac{5}{2}\). So each dose has a 2.5 ml dose.

Question 2.

A container holds 0.7 liters of oil and vinegar. \(\frac{3}{4}\) of the mixture is vinegar. How many liters of vinegar are in the container? Express your answer as both a fraction and a decimal.

Answer:

The number of liters of vinegar is in the container is \(\frac{21}{40}\) liters. And in decimals it is 0.75 × 0.7 = 0.525 liters.

Explanation:

Here, a container holds 0.7 liters of oil and vinegar and \(\frac{3}{4}\) of the mixture is vinegar, so the number of liters of vinegar is in the container is \(\frac{3}{4}\) × 0.7

= \(\frac{3}{4}\) × \(\frac{7}{10}\)

= \(\frac{21}{40}\) liters.

and in decimals it is 0.75 × 0.7 = 0.525 liters.

Question 3.

Andres completed a 5-km race in 13.5 minutes. His sister’s time was 1\(\frac{1}{2}\) times longer than his time. How long, in minutes, did it take his sister to run the race?

Answer:

His sister to run the race in 20.25 minutes.

Explanation:

Here, Andres completed a 5-km race in 13.5 minutes, and his sister’s time was 1\(\frac{1}{2}\) times longer than his time. So his sister run the race in \(\frac{1}{2}\) of 13.5 which is 0.5 × 13.5 = 6.75. And his sister to run the race in 13.5 + 6.75 which is 20.25 minutes.

Question 4.

A clothing factory uses 1,275.2 meters of cloth a week to make shirts. How much cloth is needed to make 3\(\frac{3}{5}\) times as many shirts?

Answer:

The cloth needed is 4,509.72 meters.

Explanation:

Here, a clothing factory uses 1,275.2 meters of cloth a week to make shirts which is, and the cloth needed to make shirts are 1,275.2 of 3\(\frac{3}{5}\) which is 1,275.2 × \(\frac{18}{5}\) = 4,509.72 meters.

Question 5.

There are \(\frac{3}{4}\) as many boys as girls in a class of fifth-graders. If there are 35 students in the class, how many are girls?

Answer:

The number of girls is 20 students.

Explanation:

Given that there are \(\frac{3}{4}\) as many boys as girls in a class of fifth-graders and there are 35 students in the class, so the number of girls is, as the total of 7 units are the same as 35 students and for 1 unit it will be 35 ÷ 7 which is 5 students. So the number of girls is 4 × 5 = 20 students and the number of boys is 3 × 5 = 15 students.

Question 6.

Ciro purchased a concert ticket for $56. The cost of the ticket was \(\frac{4}{5}\) the cost of his dinner. The cost of his hotel was 2\(\frac{1}{2}\) times as much as his ticket. How much did Ciro spend altogether for the concert ticket, hotel, and dinner?

Answer:

Ciro spends altogether for the concert ticket, hotel, and dinner is $266.

Explanation:

Given that Ciro purchased a concert ticket for $56 and the cost of the ticket was \(\frac{4}{5}\) the cost of his dinner is, for 4 units it is 56, so for 1 unit it will be \(\frac{56}{4}\) which is 14, and for dinner, it is 5 × 14 = 70. The cost of his hotel was 2\(\frac{1}{2}\) times as much as his ticket, so 2.5 × 56 which is 140. So altogether it will be 140 + 70 + 56 which is 266. Ciro spends altogether for the concert ticket, hotel, and dinner is $266.

### Eureka Math Grade 5 Module 4 Lesson 24 Exit Ticket Answer Key

Question 1.

An artist builds a sculpture out of metal and wood that weighs 14.9 kilograms. \(\frac{3}{4}\) of this weight is metal, and the rest is wood. How much does the wood part of the sculpture weigh?

Answer:

The wooden part is 3.725 kilograms.

Explanation:

Given that an artist builds a sculpture out of metal and wood that weighs 14.9 kilograms and \(\frac{3}{4}\) of this weight is metal, and the rest is wood. So the weight of the sculpture is, as metal part is \(\frac{3}{4}\) × 14.9 which is 11.175 kilograms and the wooden part is 14.9 – 11.175 = 3.725 kilograms.

Question 2.

On a boat tour, there are half as many children as there are adults. There are 30 people on the tour. How many children are there?

Answer:

The number of children is 10 children.

Explanation:

The total number of people is 30 and a half as many children as there are adults which means the number of children is \(\frac{1}{2}\). Let the number of adults be X and the equation is

X + X \(\frac{1}{2}\) = 30, now we will multiply both side by 2.

So 2X + X = 60,

3X = 60

X = 20.

So the number of children is \(\frac{1}{2}\) × 20 = 10 children.

### Eureka Math Grade 5 Module 4 Lesson 24 Homework Answer Key

Question 1.

Jesse takes his dog and cat for their annual vet visit. Jesse’s dog weighs 23 pounds. The vet tells him his cat’s weight is \(\frac{5}{8}\) as much as his dog’s weight. How much does his cat weigh?

Answer:

The weight of the cat is 14.375 pounds.

Explanation:

Given that Jesse takes his dog and cat for their annual vet visit and Jesse’s dog weighs 23 pounds and the vet tells him his cat’s weight is \(\frac{5}{8}\) as much as his dog’s weight. So the weight of the cat is 23 × \(\frac{5}{8}\) which is 23 × 0.625 = 14.375 pounds.

Question 2.

An image of a snowflake is 1.8 centimeters wide. If the actual snowflake is \(\frac{1}{8}\) the size of the image, what is the width of the actual snowflake? Express your answer as a decimal.

Answer:

The width of the actual snowflake is 0.225 cm.

Explanation:

Given that the image of a snowflake is 1.8 centimeters wide and the actual snowflake is \(\frac{1}{8}\) the size of the image, and the width of the actual snowflake is 1.8 × \(\frac{1}{8}\) which is 0.225 cm.

Question 3.

A community bike ride offers a short 5.7-mile ride for children and families. The short ride is followed by a long ride, 5\(\frac{2}{3}\) times as long as the short ride, for adults. If a woman bikes the short ride with her children and then the long ride with her friends, how many miles does she ride altogether?

Answer:

The adult ride and children ride altogether 38.019 miles.

Explanation:

As a community bike ride offers a short 5.7-mile ride for children and families and the short ride is followed by a long ride, 5\(\frac{2}{3}\) times as long as the short ride, for adults. So if a woman bikes the short ride with her children and then the long ride with her friends, so the adult ride is 5.7 × 5\(\frac{2}{3}\) which is 5.7 × 5.67 = 32.319. Now we will add the adult ride and children ride altogether, which is 5.7 + 32.319 = 38.019 miles.

Question 4.

Sal bought a house for $78,524.60. Twelve years later he sold the house for 2\(\frac{3}{4}\) times as much. What was the sale price of the house?

Answer:

The sale price of the house is $ 215,942.65.

Explanation:

Here, Sal bought a house for $78,524.60 and twelve years later he sold the house for 2\(\frac{3}{4}\) times as much. So the sale price of the house is 2\(\frac{3}{4}\) × 78,524.60 which is 2.75 × 78,524.60 = $ 215,942.65.

Question 5.

In the fifth grade at Lenape Elementary School, there are \(\frac{4}{5}\) as many students who do not wear glasses as those who do wear glasses. If there are 60 students who wear glasses, how many students are in the fifth grade?

Answer:

The number of students are in fifth grade is 300 students.

Explanation:

Given that there are \(\frac{4}{5}\) as many students who do not wear glasses as those who do wear glasses and the total number of students are equal with one or \(\frac{5}{5}\) which means the proportion of user who wear glasses is \(\frac{5}{5}\) – \(\frac{4}{5}\) which is \(\frac{1}{5}\) and from the information we can process (\(\frac{4}{5}\) ÷ \(\frac{5}{5}\)) × 60 on solving we will get the result as 240. So it means the total number of students in the class is accumulation between students without glasses is 240 + 60 = 300 students.

Question 6.

At a factory, a mechanic earns $17.25 an hour. The president of the company earns 6\(\frac{2}{3}\) times as much for each hour he works. The janitor at the same company earns \(\frac{3}{5}\) as much as the mechanic. How much does the company pay for all three employees’ wages for one hour of work?

Answer:

The company pay for all three employees wages for one hour of work is $142.60.

Explanation:

Given that a factory, a mechanic earns $17.25 an hour and the president of the company earns 6\(\frac{2}{3}\) times as much for each hour he works, so presidents wage is 6\(\frac{2}{3}\) × $17.25 which is $115. And the janitor at the same company earns \(\frac{3}{5}\) as much as the mechanic, so janitor wage is \(\frac{3}{5}\) × $17.25 which is $10.35. So the company pay for all three employees wages for one hour of work is $17.25 + $115 + $10.35 which is $142.60.