Answer: B
Step-by-step explanation:
Rocco: [tex]\dfrac{1}{7}[/tex] of the job per hour
Giulia: [tex]\dfrac{1}{x}[/tex] of the job per hour
Together: [tex]\dfrac{1}{3}[/tex] of the job per hour
Rocco + Giulia = Together
[tex]\dfrac{1}{7}[/tex] + [tex]\dfrac{1}{x}[/tex] = [tex]\dfrac{1}{3}[/tex]
[tex]\dfrac{1}{7}(21x)[/tex] + [tex]\dfrac{1}{x}(21x)[/tex] = [tex]\dfrac{1}{3}(21x)[/tex]
3x + 21 = 7x
21 = 4x
[tex]\dfrac{21}{4} = x[/tex]
It will take Giulia [tex]\dfrac{21}{4} = 5\dfrac{1}{4}[/tex] hours to paint the room by herself.
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Giulia: [tex]r=\dfrac{1}{x}[/tex] = [tex]\dfrac{4}{21}[/tex]
A) [tex]\dfrac{3}{7} + 3(\dfrac{4}{21}) = 7[/tex]
[tex]\dfrac{3}{7} + \dfrac{4}{7} = 7[/tex]
[tex]\dfrac{7}{7} = 7[/tex]
1 = 7
FALSE
B) [tex]\dfrac{3}{7} + 3(\dfrac{4}{21}) = 1[/tex]
[tex]\dfrac{3}{7} + \dfrac{4}{7} = 1[/tex]
[tex]\dfrac{7}{7} = 1[/tex]
1 = 1
TRUE
