Question

A spice mixture is 25% thyme. How many grams of thyme must be added to 12g of the mixture to increase the thyme content to 40%?

Answer 1

To increase the thyme content in the mixture to 40%, we need to calculate how many grams of thyme must be added. We can set up a proportion using the percentages of thyme and solve for the unknown amount of thyme using an equation.

Step-by-step explanation:

To find out how many grams of thyme must be added to the mixture, we can set up a proportion using the percentages of thyme. Let x be the amount of thyme to be added.

The current amount of thyme in the mixture is 25% of the total mixture. So, we have 25% = 0.25. The new amount of thyme in the mixture is 40% of the total mixture, which is 40% = 0.40.

Setting up the proportion, we have (12 + x) / (12 + x + x) = 0.40. Solving this equation will give us the number of grams of thyme that need to be added to the mixture.

Answer 2

3 g

Step-by-step explanation:

You want to know the mass of thyme that must be added to 12 g of a spice mix that is 25% thyme in order to make it 40% thyme.

Setup

Let t represent the amount of added thyme (in grams). The amount of thyme in the augmented mix is ...

0.25(12) + t = 0.40(12 +t)

Solution

Simplifying the equation gives ...

3 +t = 4.8 +0.40t

0.6t = 1.8 . . . . . . . . . subtract 0.40t +3

t = 3 . . . . . . . . . . . divide by 0.6

3 grams of thyme must be added to the mix.