Question

Matilda and Lorraine work in the mail room of a large company sorting letters. Matilda has already sorted 50 letters and continues sorting at a rate of 50 letters per hour. Lorraine has already sorted 80 letters and continues sorting at a rate of 40 letters per hour.

Which function can Matilda and Lorraine use to determine the total number of letters they have sorted after x hours? How many letters will they have sorted after 6 hours?

The function that describes the total number of letters sorted by Matilda and Lorraine in x hours is given by f(x) = 90x + 130. Thus, they will have sorted 670 letters in 6 hours.

The function that describes the total number of letters sorted by Matilda and Lorraine in x hours is given by f(x) = 90x + 30. Thus, they will have sorted 570 letters in 6 hours.

The function that describes the total number of letters sorted by Matilda and Lorraine in x hours is given by f(x) = 130x + 90. Thus, they will have sorted 870 letters in 6 hours.

The function that describes the total number of letters sorted by Matilda and Lorraine in x hours is given by f(x) = 100x + 120. Thus, they will have sorted 720 letters in 6 hours.

Answer 1

1) Number of letters Matilda has sorted after x hours: m(x)
Matilda has already sorted 50 letters and continues sorting at a rate of 50 letters per hour:
m(x)=50+50x
where:
Number of hours: x

Number of letters Lorraine has sorted after x hours: l(x)
Lorraine has already sorted 80 letters and continues sorting at a rate of 40 letters per hour:
l(x)=80+40x
where:
Number of hours: x

Which function can Matilda and Lorraine use to determine the total number of letters they have sorted after x hours?
Total number of letters they have sorted after x hours: f(x)

f(x)=m(x)+l(x)
f(x)=(50+50x)+(80+40x)
f(x)=50+50x+80+40x
f(x)=90x+130

Answer: The function Matilda and Lorraine can use to determine the total number of letters they have sorted after x hours is f(x)=90x+130

2) How many letters will they have sorted after 6 hours?

x=6→f(6)=?
f(6)=90(6)+130
f(6)=540+130
f(6)=670

Answer: They will have sorted 670 letters after 6 hours

Answer: First option: The function that describes the total number of letters sorted by Matilda and Lorraine in x hours is given by f(x) = 90x + 130. Thus, they will have sorted 670 letters in 6 hours.