Question 1

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

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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