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Robert mixed 1 1 3 liters of blue paint with 1 2 3 liters of red paint to make 3 liters of purple paint. To make a new batch of purple paint he used 2 liters of red paint. Using the same ratio, Robert should use Response area liters of blue paint . brainly

Sagot :

JeanaShupp

Answer: Hence, [tex]1\dfrac35[/tex] liters of blue paint have been used.

Step-by-step explanation:

Given: Robert mixed [tex]1\dfrac13[/tex] liters of blue paint with [tex]1\dfrac23[/tex] liters of red paint to make 3 liters of purple paint.

[tex]1\dfrac13=\dfrac{4}{3}\\\\ 1\dfrac23=\dfrac{5}{3}[/tex]

Ratio of blue paint to red paint = [tex]\dfrac{\dfrac{4}{3}}{\dfrac53}=\dfrac{4}{5}=4:5[/tex]

let x be the quantity of blue paint used with 2 liters of red paint..

Then

[tex]x:2=4:5\\\\\Rightarrow\ x=\dfrac{4\times2}{5}\\\\\Rightarrow\ x=\dfrac85=1\dfrac35[/tex]

Hence, [tex]1\dfrac35[/tex] liters of blue paint have been used.

The amount of blue paint used is  [tex]1\dfrac{3}{5}[/tex] liters and this can be determined by using the arithmetic operations.

Given :

  • Robert mixed [tex]1\dfrac{1}{3}[/tex] liters of blue paint with [tex]1\dfrac{2}{3}[/tex] liters of red paint to make 3 liters of purple paint.
  • To make a new batch of purple paint he used 2 liters of red paint.

Amount of Blue Paint = 4/3 liters

Amount of Red Paint = 5/3 liters

Now, the ratio of blue paint to red paint is given by:

[tex]=\dfrac{\dfrac{4}{3}}{\dfrac{5}{3}}[/tex]

[tex]=\dfrac{4}{5}[/tex]

Now, assume that the amount of blue paint that is used with 2 liters of red paint is 'a'. Then it is given that using the same ratio, Robert should use response area liters of blue paint, that is:

[tex]\dfrac{a}{2}=\dfrac{4}{5}[/tex]

[tex]a = \dfrac{8}{5}[/tex]

[tex]\rm a = 1\dfrac{3}{5} \; liters[/tex]

Therefore, it will be said that [tex]1\dfrac{3}{5}[/tex] liters of blue paint is used.

For more information, refer to the link given below:

https://brainly.com/question/544948

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