Question 1

If the sum of three consecutive even integers is $$90$$, what is the value of the smallest integer?

Accepted Answer

Question 2

Which equation correctly represents the sum of three consecutive even integers, where $$x is $$the smallest integer?

Accepted Answer

$$x + (x+2) + (x+4) = S$$

Question 3

A teacher asks students to find three consecutive even integers whose sum is $$108. $$What is the middle integer?

Accepted Answer

$$38$$

Question 4

If $$x is $$the first of three consecutive even integers and their sum is $$72$$, what is the value of $$x$$?

Accepted Answer

$$24$$

Question 5

Which of the following steps is correct when simplifying $$x + (x+2) + (x+4)$$?

Accepted Answer

$$3x + 6$$

Question 6

A real-world scenario: Three siblings are born two years apart. If the sum of their ages is $$54$$, how old is the youngest sibling?

Accepted Answer

$$18$$

Question 7

If the sum of three consecutive even integers is $$120$$, what is the value of the largest integer?

Accepted Answer

$$42$$

Question 8

Which of the following is the correct first step in solving for $$x in$$ $$x + (x+2) + (x+4) = 90$$?

Accepted Answer

Combine like terms to get $$3x + 6 = 90$$

Question 9

If $$x is $$the first even integer and $$x + (x+2) + (x+4) = 66$$, what is the value of the second integer?

Accepted Answer

$$22$$

Question 10

A chemist is mixing three solutions with volumes in consecutive even milliliters. If the total volume is $$150 mL$$, what is the volume of the smallest solution?

Accepted Answer

$$50 mL$$

Question 11

Which of the following best describes the process of finding three consecutive even integers whose sum is a given number?

Accepted Answer

Set up the equation $$x + (x+2) + (x+4) = S$$ and solve for $$x$$

Question 12

If the sum of three consecutive even integers is $$60$$, what are the integers?

Accepted Answer

$$16, 18, 20$$

Question 13

A real-life application: Three friends buy tickets to a concert, each ticket price is an even number and each is $$2$$ dollars more than the previous. If the total cost is $$90$$, what is the price of the most expensive ticket?

Accepted Answer

$$32$$

Question 14

Which of the following is a common mistake when solving for three consecutive even integers whose sum is $$S$$?

Accepted Answer

Using $$x + (x+1) + (x+2) = S$$

Question 15

If $$x is $$the first even integer and $$x + (x+2) + (x+4) = 72$$, what is the value of $$x+4$$?

Accepted Answer

$$28$$

Solving Word Problems: Consecutive Even Integers

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