A group of workers was supposed to make 768 vacuum cleaners in a certain amount of time. For the first five days, the team made exactly the number of vacuum cleaners they were supposed to make in order to be finished by their deadline. For the rest of the time they made 6 more vacuum cleaners each day than they were supposed to and so the day before the deadline they already had 844 vacuum cleaners. How many vacuum cleaners was the group supposed to make each day?

They were supposed to make 32 vacuum cleaners.

Step-by-step explanation:

Let us mark the number of the cleaners they supposed to make with x, and the number of the days they needed to work with y.

From this, we get:

x • y = 768

For the first five days, they worked on schedule (5•x), but then they started making six cleaners more each day then predicted (x+6) and they already had 844 cleaners one day before the deadline. The number of days they produced more cleaners is y minus five days they worked on schedule minus one day before the deadline when the cleaners were counted (y-6). So, that means:

5•x + (y-6)(x+6) = 844

5x + xy + 6y - 6x - 36 = 844

xy + 6y - x = 880

We already found that xy = 768, so if we subtract that from this equation we get:

6y - x = 112

If xy = 768, then x = 768/y

6y - 768/y = 112

Now, we multiply this by y:

6y^2 - 768 = 112y

6y^2 - 112y - 768 = 0

We get a quadratic equation. When we solve it, we get the solutions 24 and -5.333.

Since it's obvious that y (number of days) must be positive and integer number, the only solution is y = 24.

x = 768/y

x = 768/24

x = 32.

So, the number of vacuum cleaners the workers were supposed to make was 32.

32 vacuum cleaners.

Step-by-step explanation:

Let's call

x: the number of vacuum cleaners was the group supposed to make each day

y: the number of days they were supposed to worked

A group of workers was supposed to make 768 vacuum cleaners in a certain amount of time means:

x*y = 768 (eq. 1)

The other statement is expressed mathematically as follows:

5*x + (y-6)*(x+6)  = 844 (eq. 2)

(the first term is the production in the first five days and the second term shows that the production increased by 6 (x+6) and that they worked 5 days less until the day before the deadline (y -5 -1))

Applying distributive property to eq. 2:

5*x + y*x + 6*y - 6*x - 36 = 844

-x + y*x + 6*y = 880

Substituting eq. 1:

-x + 768 + 6*y = 880

-x + 6*y = 112

Multiplying it by y and substituting eq. 1:

-x*y + 6*y² = 112*y

0 = -6*y² + 112*y + x*y

0 = -6*y² + 112*y + 768

which can be solved with the quadratic formula:

They couldn't work -5.33 days, so the correct answer is y = 24

Replacing in equation 1:

x*24 = 768

x = 768/24 = 32

y = 5x + 17

step-by-step explanation:

a perpendicular line will be the opposite reciprocal slope of the given equation.   the slope given is -1/5 so the opposite reciprocal is 5

find b:

7 = 5 (-2) + b

7 = -10 + b

17 = b

write equation

y = 5x + 17

answer: about 22.67

step-by-step explanation: