Formulating Algebraic Expressions

The sum of two consecutive integers is 25. Which of the following represents the correct algebraic equation for this situation?

• 
  𝑥 + 𝑦 = 25

• x − y = 25

• x + ( x + 1 ) = 25

• 2x = 25

Answer explanation

The correct choice is x+(x+1)=25 because the sum of two consecutive integers can be represented as x + (x+1) = 25, where x is the first integer and x+1 is the consecutive integer.

A rectangle has a length that is 3 more than twice its width. If the perimeter of the rectangle is 40 units, which equation correctly represents this situation?

• 2x + 2( x + 3 ) = 40

• 2x + 2y = 40

• 2x + 3 = 40

• 2x + 2( 2x + 3 ) = 40

Answer explanation

Choose the equation where the length is 3 more than twice the width, which is represented by 2x+2(x+3)=40.

The total cost of purchasing x notebooks and y pens is $15. If each notebook costs $2 and each pen costs $1, what is the correct equation for this situation?

• 2x + y = 15

• x + 2y = 15

• 2x + 2y = 15

• x + y = 15

Answer explanation

To find the total cost equation, we multiply the cost of each notebook by the number of notebooks (x) and the cost of each pen by the number of pens (y), resulting in the equation x + 2y = 15.

A car travels at a constant speed. If it travels a distance of d miles in t hours, which equation represents this situation?

• d = t

• d + t = 0

• d × t = 0

• d = rt

Answer explanation

The equation d=rt represents the situation where a car travels a distance of d miles in t hours at a constant speed.

The sum of two numbers is 50, and one number is 10 more than the other. Which equation correctly represents this situation?

• x + y = 50

• x − y = 10

• x + y = 10

• x − y = 50

Answer explanation

The correct equation is x+y=50 because the sum of two numbers is 50, and one number is 10 more than the other, which translates to x+y=50.

The area of a square is 25 square units. What is the correct equation for this situation?

• x × x = 25

• x + x = 25

• 4x = 25

• 2x = 25

Answer explanation

The correct equation for the area of a square is x × x = 25, where x represents the side length of the square.

A farmer has x chickens and y cows on his farm. The total number of legs on the farm animals is 38. Which equation represents this situation?

• 2x + 4y = 38

• x + y = 38

• 2x + 2y = 38

• 4x + 2y = 38

Answer explanation

Answer Explanation highlighting the correct choice: 2x + 4y = 38

The perimeter of a triangle is 30 units. If one side is twice the length of the second side, and the third side is 5 units longer than the second side, what is the correct equation for this situation?

• x + 2x + ( x + 5 ) = 30

• x + 2x + x + 5 = 30

• 3x + 5 = 30

• 2x + x + x + 5 = 30

Answer explanation

The correct equation is x + 2x + ( x + 5 ) = 30 because the perimeter of a triangle is the sum of all three sides, where one side is twice the length of the second side and the third side is 5 units longer than the second side.

John's age is 4 times Jane's age. If their combined age is 40 years, which equation correctly represents this situation?

• x + 4x = 40

• x + 4 = 40

• x + 4y = 40

• 4x + y = 40

Answer explanation

Choose the equation x + 4x = 40 because John's age is 4 times Jane's age, and their combined age is 40 years.

If the perimeter of a rectangle is 24 units and the length is 3 units more than the width, what is the correct equation for this situation?

• 2x + 2( x + 3 ) = 24

• 2x + 2y = 24

• 2x + 3 = 24

• 2x + 2( 2x + 3 ) = 24

Answer explanation

Choose the equation that represents the perimeter of a rectangle with length 3 units more than the width, which is 2x + 2( x + 3 ) = 24