IM Alg1.2.4 Lesson: Equations and Their Solutions

A granola bite contains 27 calories. Most of the calories come from  grams of carbohydrates. The rest come from other ingredients. One gram of carbohydrate contains 4 calories. The equation  represents the relationship between these quantities. What could the 5 represent in this situation?

Priya said that neither 8 nor 3 could be the solution to the equation. Explain why she is correct.

Find the solution to the equation.

Jada has time on the weekends to earn some money. A local bookstore is looking for someone to help sort books and will pay $12.20 an hour. To get to and from the bookstore on a work day, however, Jada would have to spend $7.15 on bus fare. Write an equation that represents Jada’s take-home earnings in dollars, , if she works at the bookstore for  hours in one day.

One day, Jada takes home $90.45 after working  hours and after paying the bus fare. Write an equation to represent this situation.

Is 4 a solution to the last equation you wrote? What about 7?

• If so, be prepared to explain how you know one or both of them are solutions.
• If not, be prepared to explain why they are not solutions. Then, find the solution.

In this situation, what does the solution to the equation tell us?

Jada has a second option to earn money—she could help some neighbors with errands and computer work for $11 an hour. After reconsidering her schedule, Jada realizes that she has about 9 hours available to work one day of the weekend. Which option should she choose—sorting books at the bookstore or helping her neighbors? Explain your reasoning.

One gram of protein contains 4 calories. One gram of fat contains 9 calories. A snack has 60 calories from grams of protein and grams of fat. The equation  represents the relationship between these quantities.  Determine if this pair of values could be the number of grams of protein and fat in the snack. Be prepared to explain your reasoning. 5 grams of protein and 2 grams of fat

10.5 grams of protein and 2 grams of fat

8 grams of protein and 4 grams of fat

If there are 6 grams of fat in the snack, how many grams of protein are there? Show your reasoning.

In this situation, what does a solution to the equation  tell us? Give an example of a solution.