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A batch of lotion was made at a factory by mixing 1.3 liters of ingredient A with 2.7 liters of ingredient B in a mixing vat. By accident, a worker added an extra 0.5 liters of ingredient A to the mixing vat. How many liters of ingredi-ent B should the worker add to the mixing vat so that the ingredients will be in the original ratio

Respuesta :

MrRoyal

Answer:

The worker needs 3.74L of ingredient B

Step-by-step explanation:

Given

[tex]A:B = 1.3L:2.7L[/tex]

Required

Determine the B equivalent of (1.3L + 0.5L) of A

[tex]A:B = 1.3L:2.7L[/tex]

Convert to Fraction

[tex]\frac{A}{B} = \frac{1.3L}{2.7L}[/tex]

[tex]\frac{A}{B} = \frac{1.3}{2.7}[/tex] ----(1)

For the new mix of A

[tex]New\ A = 1.3L + 0.5L[/tex]

[tex]New\ A = 1.8L[/tex]

New A requires New B:

So:

We have:

[tex]New\ A: New\ B[/tex]

Convert this to fraction;

[tex]Ratio = \frac{New\ A}{New\ B}[/tex]

Substitut2 1.8L for New A

[tex]Ratio = \frac{1.8L}{New\ B}[/tex] --- (2)

Equate (1) and (2)

[tex]\frac{1.8L}{New\ B} = \frac{1.3}{2.7}[/tex]

Cross Multiply:

[tex]New\ B * 1.3 = 1.8L * 2.7[/tex]

Divide through by 1.3

[tex]New\ B = \frac{1.8L * 2.7}{1.3}[/tex]

[tex]New\ B = \frac{4.86L}{1.3}[/tex]

[tex]New\ B = 3.74\ L[/tex] (Approximated)

Hence;

The worker needs 3.74L of ingredient B