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

The worker needs 3.74L of ingredient B

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

`(A)/(B) = (1.3L)/(2.7L)`

`(A)/(B) = (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 = (New\ A)/(New\ B)`

Substitut2 1.8L for New A

`Ratio = (1.8L)/(New\ B)` --- (2)

Equate (1) and (2)

`(1.8L)/(New\ B) = (1.3)/(2.7)`

Cross Multiply:

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

Divide through by 1.3

`New\ B = (1.8L * 2.7)/(1.3)`

`New\ B = (4.86L)/(1.3)`

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

Hence;

The worker needs 3.74L of ingredient B