Production of trailers

An automobile factory produced trailers. In the first quarter it produced a fifth of the annual production, in the second quarter it produced half more than in the first quarter, in the third quarter it produced 13 000 trailers more than in the second quarter, and in the fourth quarter it produced half of what it produced in the second quarter.

Calculate how many trailers the automobile factory produced for the entire year.
Calculate how many it produced in the quarter when the number of trailers was the highest.

Final Answer:

x =  260000
y =  91000

Step-by-step explanation:


a+b+c+d = x
a = x/5
b = a + a/2
c = 13000 + b
d = b/2

a+b+c+d-x = 0
5a-x = 0
3a-2b = 0
b-c = -13000
b-2d = 0

Pivot: Row 1 ↔ Row 2
5a-x = 0
a+b+c+d-x = 0
3a-2b = 0
b-c = -13000
b-2d = 0

Row 2 - 1/5 · Row 1 → Row 2
5a-x = 0
b+c+d-0.8x = 0
3a-2b = 0
b-c = -13000
b-2d = 0

Row 3 - 3/5 · Row 1 → Row 3
5a-x = 0
b+c+d-0.8x = 0
-2b+0.6x = 0
b-c = -13000
b-2d = 0

Pivot: Row 2 ↔ Row 3
5a-x = 0
-2b+0.6x = 0
b+c+d-0.8x = 0
b-c = -13000
b-2d = 0

Row 3 - 1/-2 · Row 2 → Row 3
5a-x = 0
-2b+0.6x = 0
c+d-0.5x = 0
b-c = -13000
b-2d = 0

Row 4 - 1/-2 · Row 2 → Row 4
5a-x = 0
-2b+0.6x = 0
c+d-0.5x = 0
-c+0.3x = -13000
b-2d = 0

Row 5 - 1/-2 · Row 2 → Row 5
5a-x = 0
-2b+0.6x = 0
c+d-0.5x = 0
-c+0.3x = -13000
-2d+0.3x = 0

Row 4 + Row 3 → Row 4
5a-x = 0
-2b+0.6x = 0
c+d-0.5x = 0
d-0.2x = -13000
-2d+0.3x = 0

Pivot: Row 4 ↔ Row 5
5a-x = 0
-2b+0.6x = 0
c+d-0.5x = 0
-2d+0.3x = 0
d-0.2x = -13000

Row 5 - 1/-2 · Row 4 → Row 5
5a-x = 0
-2b+0.6x = 0
c+d-0.5x = 0
-2d+0.3x = 0
-0.05x = -13000


x = -13000/-0.05 = 260000
d = 0-0.3x/-2 = 0-0.3 · 260000/-2 = 39000
c = 0-d+0.5x = 0-39000+0.5 · 260000 = 91000
b = 0-0.6x/-2 = 0-0.6 · 260000/-2 = 78000
a = 0+x/5 = 0+260000/5 = 52000

a = 52000
b = 78000
c = 91000
d = 39000
x = 260000

Our linear equations calculator calculates it.
y=max(a,b,c,d)=max(52000,78000,91000,39000)=91000



Help us improve! If you spot a mistake, please let let us know. Thank you!







Tips for related online calculators
Do you have a linear equation or system of equations and are looking for a solution? Or do you have a quadratic equation?

You need to know the following knowledge to solve this word math problem:

algebrabasic operations and conceptsGrade of the word problem

Related math problems and questions: