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

Feb 25, 2017

We must add $3$ g of thyme

#### Explanation:

As spice mixture is 25% thyme, in $12$ g of the mixture

we have $12 \times \frac{25}{100} = 3$ g of thyme.

If we add $x$ g of thyme,

we have $x + 3$ g of thyme and $12 + x$ g of mixture

but this should be 40%=40/100

Hence $\frac{x + 3}{12 + x} = \frac{40}{100}$

i.e. $100 x + 300 = 480 + 40 x$

or $100 x - 40 x = 480 - 300$

or $60 x = 180$

i.e. $x = \frac{180}{60} = 3$

Hence, we must add $3$ g of thyme

then we have $6$ g of thyme in $15$ g of mixture.