Question

1. match the situation with its equation.

the sum of three consecutive integers is 54.
let $x$ represent the smallest integer.

the sum of three consecutive even integers is 54.
let $x$ represent the smallest integer.

the sum of four consecutive integers is 54.
let $x$ represent the smallest integer.

the width of a rectangular garden is 2 feet longer than the length.
the perimeter is 54 feet.
let $x$ represent the length of the garden.

the perimeter of a square garden is 54 feet.
let $x$ represent the side length of the garden.

$x+(x+2)+(x+4)=54$
$x+(x+2)+x+(x+2)=54$
$x+(x+1)+(x+2)+(x+3)=54$
$x+(x+1)+(x+2)=54$
$x+x+x+x=54$

Explanation:

Step1: Match 3 consecutive integers

Consecutive integers differ by 1. If smallest is $x$, the three are $x$, $x+1$, $x+2$. Sum equation: $x+(x+1)+(x+2)=54$

Step2: Match 3 consecutive even integers

Consecutive even integers differ by 2. If smallest is $x$, the three are $x$, $x+2$, $x+4$. Sum equation: $x+(x+2)+(x+4)=54$

Step3: Match 4 consecutive integers

Consecutive integers differ by 1. If smallest is $x$, the four are $x$, $x+1$, $x+2$, $x+3$. Sum equation: $x+(x+1)+(x+2)+(x+3)=54$

Step4: Match rectangular garden perimeter

Width = $x+2$ (length $x$). Perimeter formula: $2(\text{length}+\text{width})$. Substitute: $2(x + x+2)=x+(x+2)+x+(x+2)=54$

Step5: Match square garden perimeter

Square has 4 equal sides $x$. Perimeter: $x+x+x+x=54$

Answer:

1. The sum of three consecutive integers is 54. (Let $x$ represent the smallest integer.) $\boldsymbol{\longleftrightarrow}$ $x+(x+1)+(x+2)=54$
2. The sum of three consecutive even integers is 54. (Let $x$ represent the smallest integer.) $\boldsymbol{\longleftrightarrow}$ $x+(x+2)+(x+4)=54$
3. The sum of four consecutive integers is 54. (Let $x$ represent the smallest integer.) $\boldsymbol{\longleftrightarrow}$ $x+(x+1)+(x+2)+(x+3)=54$
4. The width of a rectangular garden is 2 feet longer than the length. The perimeter is 54 feet. (Let $x$ represent the length of the garden.) $\boldsymbol{\longleftrightarrow}$ $x+(x+2)+x+(x+2)=54$
5. The perimeter of a square garden is 54 feet. (Let $x$ represent the side length of the garden.) $\boldsymbol{\longleftrightarrow}$ $x+x+x+x=54$