Respuesta :
Answer:
50.87 : 66.13.
Step-by-step explanation:
10/(10+13) * 117
= 10 * 117 / 23
= 50.87.
117 - 50.87 = 66.13.
When 117 kg is decreased in 10:13, then it is partitioned in two parts, first part being of 50.87 kg and second part being of 66.13 kg approximately.
What is ratio of two quantities?
Suppose that we've got two quantities with measurements as 'a' and 'b'
Then, their ratio(ratio of a to b) a:b or [tex]\dfrac{a}{b}[/tex]
We usually cancel out the common factors from both the numerator and the denominator of the fraction we obtained. Numerator is the upper quantity in the fraction and denominator is the lower quantity in the fraction).
Suppose that we've got a = 6, and b= 4, then:
[tex]a:b = 6:2 = \dfrac{6}{2} = \dfrac{2 \times 3}{2 \times 1} = \dfrac{3}{1} = 3\\or\\a : b = 3 : 1 = 3/1 = 3[/tex]
Remember that the ratio should always be taken of quantities with same unit of measurement. Also, ratio is a unit-less(no units) quantity.
Therefore, suppose the given 117 kg of amount is divided in two parts viz [tex]x \: \rm kg[/tex] and [tex]y \: \rm kg[/tex] having ratio as 10:13
Then, we get two equations as:
[tex]x + y = 117[/tex]
[tex]\dfrac{x}{y} = \dfrac{10}{13}[/tex]
From the second equation, we get x in terms of y as:
[tex]\dfrac{x}{y} = \dfrac{10}{13}\\\\\text{Multiplying y on both the sides}\\\\x = \dfrac{10y}{13}[/tex]
Putting this value of x in first equation, we get:
[tex]x + y = 117\\\\\dfrac{10y}{13} + y = 117\\\\\dfrac{10y + 13y}{13} = 117\\\\23y = 117 \times 13\\y = \dfrac{1521}{23} \approx 66.13[/tex] (in kg)
And therefore, from the expression for x, we get:
[tex]x = \dfrac{10y}{13} \approx \dfrac{10 \times 66.13}{13} \approx 50.87[/tex] (in kg)
Thus, when 117 kg is decreased in 10:13, then it is partitioned in two parts, first part being of 50.87 kg and second part being of 66.13 kg approximately.
Learn more about ratio here:
brainly.com/question/186659
