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Sagot :
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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