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Linear Equations Part 1

HS: High School

Created on June 29, 2023

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Transcript

Linear Equations Part 1

Use the 3 following scenarios to help you write and solve equations for your project. Click the "+" button to learn more at each scenario.

Scenario 1

Scenario 3

Breakfast Foods!

Bean Stalk!

Scenario 2

Losing Water!

Breakfast Food!

Amara buys a pack of Honey Buns for $3. She also buys 7 different boxes of cereal, each marked the same price. Amara spends a total of $31. Let x represent the cost of the cereal boxes. How much did each box of cereal cost? We wrote the equation last week: 7x + 3 = 31 Now let's solve for x, the cost of the cereal boxes. 7x + 3 = 31 Subtract 3 from both sides 7x = 28 Divide both sides by 7 x = 4 So we now know that each box of cereal costs $4.

Bean Stalk!

At the beginning of an experiment, a biologist measures the height of a bean stalk to be 3.8 centimeters tall. The bean stalk is growing at a rate of 0.7 centimeters per day. If the bean stalk continues to grow at this rate, how many days will it take for the bean stalk to be 18.5 cm tall?

If the total height is 18.5 tall, how many days?

  • Use the equation y = 0.7x + 3.8
  • Substitute y = 18.5 cm
  • 18.5 = 0.7x + 3.8
  • 14.7 = 0.7x
  • 21 = x
After 21 days, the bean stalk will be 18.5 centimeters tall.

WRITE THE EQUATION TO DESCRIBE SITUATION We know the bean stalk grows 0.7 centimeters/day and the height of the stalk to start is 3.8 cm. y = total centimeters, x = days Therfore the equation to find the total height of the plant would be: y = 0.7x + 3.8

Losing Water!

A swimming pool containing 5000 gallons of water loses water at a rate of 3 gallons per minute.

WRITE AN EQUATION TO DESCRIBE SITUATION We know the pool is losing 3 gallons of water per minute LOSING means negative! And we start with 5000 gallons of water in the pool to start. y = total gallons left in the pool , x = minutes We write our equation: y = -3x + 5000 After 30 minutes, there are 4910 gallons remaining in the pool.

AFTER 30 MINUTES? Use the equation y = -3x + 5000 Substitute x = 30 minutes y = -3 (30) + 5000 y = -90 + 5000 y = 4910