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The total volume of one bottle of shampoo and one bottle of conditioner was 845 milliliters. When Marco washed his hair, he used 2/35 of the shampoo and 4/45 of the conditioner, a total of 64 milliliters.

What are the values of x, the total initial volume of shampoo, and y, the total initial volume of conditioner?
A. 350mL of shampoo and 495 mL of conditioner
B. 495 mL of shampoo and 350 mL of conditioner
C. 325 mL of shampoo and 520 mL of conditioner
D. 520 mL of shampoo and 325 mL of conditioner

Respuesta :

AutumnJoy12

Answer:

I think it is B

Step-by-step explanation:


sortingsteering

Answer: A) 350mL of shampoo and 495 mL of conditioner.

Step-by-step explanation: this problem is solved by a system of two equations, the first one will be the sum of the volumes of the two bottles that equals 845 milliliters:

x+y=845

and the second one will be the sum of the used fractions of shampoo and conditioner, that equals 64 milliliters:

[tex]\frac{2}{35}x+\frac{4}{45} y=64[/tex]

so, for the first equation we have that:

x=845-y

and we substitute this expression into the second equation:

[tex]\frac{2}{35} (845-y)+\frac{4}{45} y=64[/tex]

and we solve:

[tex]\frac{1690}{35}-\frac{2}{35}y +\frac{4}{45} y=64\\\\[/tex]

[tex]\frac{1690}{35}+(\frac{-18y+28y}{315})=64[/tex]

[tex]\frac{1690}{35} +\frac{10y}{315}=64[/tex]

[tex]\frac{2y}{63}=64-\frac{1690}{35}[/tex]

[tex]\frac{2y}{63}=\frac{110}{7}[/tex]

y=495

now with the first equation:

x=845-y

x=845-495

x=350

The shampoo is 350ml and the conditioner is 495ml.

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