Answer :
Answer:
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.
Answer:
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:
[tex]y = \frac{-b \pm \sqrt{b^2 - 4(a)(c)}}{2(a)} [/tex]
[tex]y = \frac{-112 \pm \sqrt{112^2 - 4(-6)(768)}}{2(-6)} [/tex]
[tex]y = \frac{-112 \pm 176}{-12} [/tex]
[tex]y_1 = \frac{-112 + 176}{-12} [/tex]
[tex]y_1 = -5.33[/tex]
[tex]y_2 = \frac{-112 - 176}{-12} [/tex]
[tex]y_2 = 24[/tex]
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