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Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks.Mr. Ballard and Ms. Hong are teaching their classes how to write in cursive. Mr. Ballard has already taught his class letters. The students in Ms. Hong's class, who started the unit later, currently know how to write letters. Mr. Ballard plans to teach his class new letters per week, and Ms. Hong intends to cover new letters per week. Eventually, the students in both classes will know how to write the same number of letters. How long will that take? How many letters will the students know?In weeks, the students in both classes will know how to write letters in cursive.
Full solution
Q. Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks.Mr. Ballard and Ms. Hong are teaching their classes how to write in cursive. Mr. Ballard has already taught his class letters. The students in Ms. Hong's class, who started the unit later, currently know how to write letters. Mr. Ballard plans to teach his class new letters per week, and Ms. Hong intends to cover new letters per week. Eventually, the students in both classes will know how to write the same number of letters. How long will that take? How many letters will the students know?In weeks, the students in both classes will know how to write letters in cursive.
- Define Variables: Let's define the variables:Let represent the number of weeks.Let represent the total number of letters learned by the students.For Mr. Ballard's class:Initial letters learned: Letters learned per week: Total letters learned over time:
- Mr. Ballard's Class: For Ms. Hong's class:Initial letters learned: Letters learned per week: Total letters learned over time:
- Ms. Hong's Class: Now we have two equations:) (Mr. Ballard's class)) (Ms. Hong's class)We will use substitution to solve for by setting the two equations equal to each other since represents the same total number of letters learned in both classes.
- Use Substitution: Solve for :So, it will take weeks for the students in both classes to know the same number of letters.
- Solve for x: Now we need to find out how many letters that will be. We can substitute into either of the original equations. Let's use the first equation:Therefore, after weeks, the students in both classes will know how to write letters in cursive.
