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A scientist removed a sample of 39.1 grams of a chemical from a container. The sample was \(5 \frac{3}{4}\) grams less than \(\frac{3}{10}\) of the total mass of the chemical in the container.

What was the total mass, in grams, of the chemical in the container before the scientist removed the sample of 39.1 grams?

Answer :

The total mass was 149.5 grams.

Setting up an equation, we have that the sample size, 39.1, is 5 3/4 (5.75) grams less than 3/10 of the total mass; this gives us

39.1 = 3/10x - 5.75

Adding 5.75 to both sides, we have
44.85 = 3/10x

Multiplying both sides by 10,
448.5 = 3x

Dividing both sides by 3,
149.5 = x

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Rewritten by : Barada

Using the appropriate, arithmetic operations, the total mass of chemical in the container is 149.5 grams.

Let :

  • Total mass of chemical in container = m
  • Mass of sample = 39.1

We can expression the scenario Mathematically thus ;

0.3m - 5.75 = 39.1

Solve for m

0.3m = 39.1 + 5.75

0.3m = 44.85

Divide both sides by 0.3

m = 44.85 / 0.3

m = 149.5 grams

Hence, the total mass of chemical in the container is 149.5 grams.

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