Question

Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.Mr. Larsen and Ms. Ortega are teaching their classes how to write in cursive. Mr. Larsen has already taught his class 5 letters. The students in Ms. Ortega's class, who started the unit later, currently know how to write 12 letters. Mr. Larsen plans to teach his class 2 new letters per week, and Ms. Ortega intends to cover 1 new letter 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?

Answer 1

Given:

5 letters were completed in Mr. Larsen's class.

12 letters were completed in Ms. Ortega's class.

Mr. Larsen plans to teach his class 2 new letters per week, and Ms. Ortega intends to cover 1 new letter per week.

Mr. LarsenLet x be the number of letters learned in Mr. Larsen's class.

Let y be the number of letters learned in Ms. Ortega's class.

Let t be the number of weeks.

`x=5+2t`
`y=12+(1)t`

The same number of letters learned after t weeks. So x=y.

Set x=y, to find the value for t.

`5+2t=12+t`

Subtracting t from both sides, we get

`5+2t-t=12+t-t`

`5+t=12`

Subtracting 5 from both sides, we get

`5+t-5=12-5`
`t=7\text{ w}eeks`

After 7 weeks the students in both classes will know how to write the same number of letters

Substitute t=7 in x to find the number of letters.

`x=5+2*7`
`x=5+14`
`x=19\text{ letters}`

The students know 19 letters.

Hence after 7 weeks, the students in both classes will know how to write 19 letters.