Question

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

Answer 1

Answer:

The worker needs 3.74L of ingredient B

Step-by-step explanation:

Given

$A:B = 1.3L:2.7L$

Required

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

$A:B = 1.3L:2.7L$

Convert to Fraction

$\frac{A}{B} = \frac{1.3L}{2.7L}$

$\frac{A}{B} = \frac{1.3}{2.7}$ ----(1)

For the new mix of A

$New\ A = 1.3L + 0.5L$

$New\ A = 1.8L$

New A requires New B:

So:

We have:

$New\ A: New\ B$

Convert this to fraction;

$Ratio = \frac{New\ A}{New\ B}$

Substitut2 1.8L for New A

$Ratio = \frac{1.8L}{New\ B}$ --- (2)

Equate (1) and (2)

$\frac{1.8L}{New\ B} = \frac{1.3}{2.7}$

Cross Multiply:

$New\ B * 1.3 = 1.8L * 2.7$

Divide through by 1.3

$New\ B = \frac{1.8L * 2.7}{1.3}$

$New\ B = \frac{4.86L}{1.3}$

$New\ B = 3.74\ L$ (Approximated)

Hence;

The worker needs 3.74L of ingredient B