## 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. Janetâ€™s brother is eight years younger than their sister Julie. The sum of all of their ages is 55 years.

Answer:

Let x be Julieâ€™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=\(\frac{1}{3}\)âˆ™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.