Algebra Application Problems

The width of a rectangle is x+3 and the length is 2x+1. Write an expression to represent the perimeter of the rectangle. Check all that are valid expressions.

• (x+3)(2x+1)

• 2x²+7x+3

• x + 3 + 2x + 1 + x + 3 + 2x + 1

• 3x + 4

• 6x + 8

The width of a rectangle is x+3 and the length is 2x+1. Write an expression to represent the area of the rectangle. Check all that are valid expressions.

• (x+3)(2x+1)

• 2x²+7x+3

• 2x²+3

• 3x + 4

• x + 3 = 2x + 1

The width of a rectangle is 4a+3 and the length is 7a -1. The perimeter is 35. Write an equation that could be used to find the value of a. Check all that apply.

• 4a + 3 + 7a - 1+ 4a + 3 + 7a - 1 = 35

• 2(4a + 3) + 2(7a - 1) = 35

• 22a⁴ + 4 = 35

• 22a + 4 = 35

• 11a + 2 = 35

The length of a rectangle is 4a+3 and the width is 7a -1. The area is 35. Write an equation that could be used to find the value of a. Check all that apply.

• 4a + 3 + 7a - 1+ 4a + 3 + 7a - 1 = 35

• (4a+3)(7a-1) = 35

• 28a² - 3 = 35

• 28a² + 17a - 3 = 35

• No equation can be written to find a

Four consecutive even integers have a sum of 172. Write an equation to find the integers. Check all that are valid equations.

• x + x + 1 + x + 2 + x + 3 = 172

• x + x + 2 + x + 4 + x + 6 = 172

• 4x + 12 = 172

• 4x⁴ + 12 = 172

• No equation can be written. It would require 4 variables.

The product of a number and the sum of 4 times the number and 5 is 125. Write an equation to find the number.

• n(4n)(5) = 125

• n + 4n + 5 = 125

• n(4n + 5) = 125

• n + 4n(5) = 125

• No equation can be written. Not enough information.

Steve and Sally are both selling candy bars. Steve has sold 8 less than 3 times the number of candy bars that Sally has sold.Together they have sold 32 candy bars. Check all equations that could be written to find out how many candy bars Sally has sold.

• 3n - 8 = 32

• n + 3n - 8 = 32

• 3n - 8 + n = 32

• n + n - 8 = 32

For the election, in one district, 2500 people voted prior to election day. If 130 people vote every hour on election day, write an equation to show how many total people will have voted in this district at the end of the election.

• y = 2500 - 130x

• 130x + 2500 = y

• 130x = 2500

• x + 130 = 2500

A craft fair charges $50 for crafters to rent a booth. A local crafter is selling all of her items for $10. Write an equation to show how much money the crafter might make at the craft fair.

• y = 10x + 50

• y = 10x - 50

• 10x + y = 50

• y - 10 = 50(x - 7)

• No equation can be written.

A craft fair charges a fee for crafters to rent a booth. A local crafter sold 25 items and made a total profit of $175. After selling 40 items, the crafter had made a profit of $325. Write an equation that the crafter could use to predict her future profits at the craft fair.

• y = 10x + 75

• y - 325 = 10(x - 40)

• y - 25 = 10(x - 175)

• y = 10x - 75

• y = 40x + 325