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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%?

Answer 1

Owen Ambrose

We must add #3# g of thyme

Thyme makes up 25% of the spice mixture in 12.1 g of the mixture.

we have #12xx25/100=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 #(x+3)/(12+x)=40/100#

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

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

or #60x=180#

i.e. #x=180/60=3#

Hence, we must add #3# g of thyme

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

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Answer 2

Kai Bowman

To increase the thyme content to 40%, you need to add ( \frac{40% - 25%}{100%} ) of the total weight as thyme. This is ( \frac{40% - 25%}{100%} \times (12 g) = 1.8 ) grams of thyme. Therefore, you need to add 1.8 grams of thyme to the mixture.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.