Linear Word Problem

You have only nickels (x) and dimes (y) in your piggy bank. When you ran the coins through a change counter, it indicated you have 595 cents. Write an equation to represent this situation.

• 5x + 10y = 595

• 10x + 5y = 595

• .05x + .10y = 595

• y = 2x + 595

Two farmers use combines to harvest corn from their fields. One farmer can harvest 600 acres of corn per day, and the other farmer can harvest 1000 acres of corn per day. They harvested 9800 acres of corn total. Which equations could represent this situation? Choose all that apply.

• 600x + 1000y = 9800

• 1000x + 600y = 9800

• y = 6/10x + 9800

• y = 10/6x + 9800

Karissa earns $200 per week plus $25 per item she sells. Which form of a linear equation would best represent the relationship between the number of items she sells (x) and her pay per week (y)?

• Standard Form

• Slope Intercept Form

• Point Slope Form

• None of the above

Hudson is already 40 miles away from home on his drive back to college. He is driving 65 mi/h. Write an equation that models the total distance y after x hours.

• y = 40x + 65

• y = 65x + 40

• 40x + 65y = 105

• y - 40 = 65(x - 0)

A sign says that 3 tickets cost $22.50 and that 7 tickets cost $52.50. Which equations in point-slope form would represents the cost of tickets? Select all that apply.

• y - 22.50 = 7.50(x - 3)

• y - 52.50 = 7.50(x - 7)

• y = 7.50x

• y + 22.50 = 7.50(x + 3)

The population of a city increases by 4000 people each year. In 2025, the population is projected to be 450,000 people. What is an equation that gives the city's population y (in thousands of people) x years after 2010?

• y = 4x + 450

• y - 450 = 4(x - 15)

• y - 15 = 4(x - 450)

• y = 4x + 15

A pizza parlor charges $1.75 per topping, and a pizza with 5 toppings cost $14.25. What form of a linear equation would best represent this situation?

• Standard Form

• Point-Slope Form

• Slope- Intercept Form

• None of the above

Cheryl is planning to spend $75 on a Christmas gift for her father. He needs new socks and ties. A store has socks and ties on sale for $4 and $11, respectively. What form of a linear equation would best represent this situation?

• Standard Form

• Point-Slope Form

• Slope-Intercept Form

• None of the above

A football team scores 63 points. All of the points come from field goals (x) worth 3 points and touchdowns (y) worth 7 points. Write an equation in standard form that represents this situation. Then convert it to slope-intercept form. Select the correct standard form and slope-intercept form.

• 3x + 7y = 63

• 7x + 3y = 63

A holiday meal costs $12.50 a person plus a delivery fee of $30. Which equation represents the amount a holiday meal costs, including delivery, for x people?

• y = 12.5x + 30

• y = 12.5 + 30

• y = 12.5 + 30x