## 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 \(\frac{1}{8}\) Ã— 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 Ã— 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 \(\frac{3}{4}\) Ã— 0.7

= \(\frac{3}{4}\) Ã— \(\frac{7}{10}\)

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

and in decimals it is 0.75 Ã— 0.7 = 0.525 liters.

Question 3.

Andres completed a 5-km race in 13.5 minutes. His sisterâ€™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 sisterâ€™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 Ã— 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 Ã— \(\frac{18}{5}\) = 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 Ã· 7 which is 5 students. So the number of girls is 4 Ã— 5 = 20 students and the number of boys is 3 Ã— 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 Ã— 14 = 70. The cost of his hotel was 2\(\frac{1}{2}\) times as much as his ticket, so 2.5 Ã— 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 \(\frac{3}{4}\) Ã— 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 \(\frac{1}{2}\) Ã— 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. Jesseâ€™s dog weighs 23 pounds. The vet tells him his catâ€™s weight is \(\frac{5}{8}\) as much as his dogâ€™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 Jesseâ€™s dog weighs 23 pounds and the vet tells him his catâ€™s weight is \(\frac{5}{8}\) as much as his dogâ€™s weight. So the weight of the cat is 23 Ã— \(\frac{5}{8}\) which is 23 Ã— 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 Ã— \(\frac{1}{8}\) 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 isÂ 5.7 Ã—Â 5\(\frac{2}{3}\) which is 5.7 Ã— 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\(\frac{3}{4}\) Ã— 78,524.60 which is 2.75 Ã— 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 (\(\frac{4}{5}\) Ã· \(\frac{5}{5}\)) Ã— 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 employeesâ€™ 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\(\frac{2}{3}\) Ã— $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 \(\frac{3}{5}\) Ã— $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.