The first group was responsible for making 160 suits while the second group was responsible for making 25% fewer suits in the same amount of time. The first team made 10 more suits each day than the second team and finished its job 2 days before the deadline date. How many suits did the second team make each day if it needed two days extra after the deadline to finish the assigned job?

group 1: 160 suits

group 2: 3/4 * 160 = 120 suits

If the 2nd team made x suits per day, then since it took 4 more days,

160/(x+10) + 4 = 120/x
x = 10

extra credit: how many days did the teams work?

To solve this problem, let's break it down step by step.

Let's assume that the second team made X suits each day.

The first group made 10 more suits each day than the second group, so they made X + 10 suits each day.

Now, let's calculate the total number of suits made by the first group. Since they finished 2 days before the deadline, we can multiply the number of days it took them by the number of suits they made each day:

Total suits made by the first group = (X + 10) * (number of days taken by the first group)

The second group took 2 days extra after the deadline to finish the job. So, the number of days taken by the second group is equal to the number of days taken by the first group + 2:

Number of days taken by the second group = (number of days taken by the first group) + 2

Now, let's calculate the total number of suits made by the second group:

Total suits made by the second group = X * (number of days taken by the second group)

We know that the second group made 25% fewer suits than the first group. This means that the total suits made by the second group is 75% (or 0.75) of the total suits made by the first group. So, we can write the equation:

Total suits made by the second group = 0.75 * Total suits made by the first group

Now, let's combine the equations:

X * (number of days taken by the second group) = 0.75 * (X + 10) * (number of days taken by the first group)

We also know that the first group made 160 suits:

Total suits made by the first group = 160

Now, we can substitute this value into the equation:

X * (number of days taken by the second group) = 0.75 * (X + 10) * (number of days taken by the first group) = 0.75 * (X + 10) * (160 / (X + 10))

Simplifying the equation by canceling out (X + 10):

X * (number of days taken by the second group) = 0.75 * 160

Simplifying further:

X * (number of days taken by the second group) = 120

Since we know that the second group needed two extra days after the deadline to finish, we can substitute the value (number of days taken by the second group) + 2 into the equation:

X * ((number of days taken by the second group) + 2) = 120

Simplifying further:

X * ((number of days taken by the second group) + 2) = 120

Now, we can solve this equation to find the value of X, which represents the number of suits the second group made each day.

Let's define some variables to solve this problem:

Let's call "X" the number of suits made by the first team each day.
Let's call "Y" the number of suits made by the second team each day.

According to the problem, the first team made 10 more suits each day than the second team. Therefore, we can write the equation:

X = Y + 10 ---(equation 1)

The first team finished the job 2 days before the deadline, while the second team needed an additional 2 days to finish the assigned job after the deadline. So essentially, the first team worked for (2 + 2 = 4) days fewer than the second team. Now, let's set up another equation:

(X * D1) = (Y * D2) + 25%*(Y * D2) ---(equation 2)

In equation 2, D1 represents the number of days the first team worked, and D2 represents the number of days the second team worked. The second term on the right side represents 25% fewer suits made by the second team.

We also know that the first team made 160 suits, so we can write the equation:

X * D1 = 160 ---(equation 3)

Considering that the second team needed an additional two days after the deadline to finish its assigned job, we can write:

(X * D1) = (Y * D2) + (Y * 2) ---(equation 4)

Now, we have a system of equations consisting of equations 1, 3, and 4. Let's solve it step-by-step:

From equation 1, we have X = Y + 10

Substitute this value of X into equation 3:

(Y + 10) * D1 = 160
Y * D1 + 10 * D1 = 160 ---(equation 5)

Substitute this value of (Y * D1) into equation 4:

160 = (Y * D2) + (Y * 2) + 10 * D1 ---(equation 6)

Since we know that the second team needed two extra days to finish the job, we can rewrite equation 6 as:

160 = (Y * (D2 + 2)) + 10 * D1 ---(equation 7)

From equation 6 and equation 7, we can conclude:

(Y * D2) + (Y * 2) + 10 * D1 = (Y * (D2 + 2)) + 10 * D1

Expanding the equation, we get:

(Y * D2) + (Y * 2) + 10 * D1 = Y * D2 + Y * 2 + 10 * D1

Simplify the equation:

(Y * 2) = (Y * 2)

We can see that both sides are equal. So, the equation does not provide any additional information.

Now, substitute the value of (Y * D1) from equation 5 into equation 4:

(Y * D2) + (Y * 2) + 10 * D1 = (Y * D2) + (Y * 2) + 10 * D1

Since both sides of the equation are equal, this equation is also redundant.

Therefore, we cannot find the specific value of Y (the number of suits made by the second team each day) using the given information.