## Engage NY Eureka Math 8th Grade Module 4 Lesson 1 Answer Key

### Eureka Math Grade 8 Module 4 Lesson 1 Exercise Answer Key

Write each of the following statements using symbolic language.

Exercise 1.

The sum of four consecutive even integers is -28.

Answer:

Let x be the first even integer. Then, x+x+2+x+4+x+6=-28.

Exercise 2.

A number is four times larger than the square of half the number.

Answer:

Let x be the number. Then, x=4(\(\frac{x}{2}\))^{2}.

Exercise 3.

Steven has some money. If he spends $9.00, then he will have \(\frac{3}{5}\) of the amount he started with.

Answer:

Let x be the amount of money (in dollars) Steven started with. Then, x-9=\(\frac{3}{5}\) x.

Exercise 4.

The sum of a number squared and three less than twice the number is 129.

Answer:

Let x be the number. Then, x^{2}+2x-3=129.

Exercise 5.

Miriam read a book with an unknown number of pages. The first week, she read five less than \(\frac{1}{3}\) of the pages. The second week, she read 171 more pages and finished the book. Write an equation that represents the total number of pages in the book.

Answer:

Let x be the total number of pages in the book. Then, \(\frac{1}{3}\) x-5+171=x.

### Eureka Math Grade 8 Module 4 Lesson 1 Problem Set Answer Key

Students practice transcribing written statements into symbolic language.

Write each of the following statements using symbolic language.

Question 1.

Bruce bought two books. One book costs $4.00 more than three times the other. Together, the two books cost him $72.

Answer:

Let x be the cost of the less expensive book. Then, x+4+3x=72.

Question 2.

Janet is three years older than her sister Julie. Janet’s brother is eight years younger than their sister Julie. The sum of all of their ages is 55 years.

Answer:

Let x be Julie’s age. Then, (x+3)+(x-8)+x=55.

Question 3.

The sum of three consecutive integers is 1,623.

Answer:

Let x be the first integer. Then, x+(x+1)+(x+2)=1623.

Question 4.

One number is six more than another number. The sum of their squares is 90.

Answer:

Let x be the smaller number. Then, x^{2}+(x+6)^{2}=90.

Question 5.

When you add 18 to \(\frac{1}{4}\) of a number, you get the number itself.

Answer:

Let x be the number. Then, \(\frac{1}{4}\) x+18=x.

Question 6.

When a fraction of 17 is taken away from 17, what remains exceeds one-third of seventeen by six.

Answer:

Let x be the fraction of 17. Then, 17-x=\(\frac{1}{3}\)∙17+6.

Question 7.

The sum of two consecutive even integers divided by four is 189.5.

Answer:

Let x be the first even integer. Then, \(\frac{x+(x+2)}{4}\)=189.5.

Question 8.

Subtract seven more than twice a number from the square of one-third of the number to get zero.

Answer:

Let x be the number. Then, (\(\frac{1}{3}\) x)^{2}-(2x+7)=0.

Question 9.

The sum of three consecutive integers is 42. Let x be the middle of the three integers. Transcribe the statement accordingly.

Answer:

(x-1)+x+(x+1)=42

### Eureka Math Grade 8 Module 4 Lesson 1 Exit Ticket Answer Key

Write each of the following statements using symbolic language.

Question 1.

When you square five times a number, you get three more than the number.

Answer:

Let x be the number. Then, (5x)^{2}=x+3.

Question 2.

Monica had some cookies. She gave seven to her sister. Then, she divided the remainder into two halves, and she still had five cookies left.

Answer:

Let x be the original amount of cookies. Then, \(\frac{1}{2}\) (x-7)=5.