Word Problem College Algebra Question

Question

During a hiking trip, Carol ran out of trail mix. She needs another 30 grams to finish the hike. Fortunately, Steve and Grace are willing to share some of their trail mix, but Carol insists on a trail mix that is precisely 50% peanuts, which neither of them has. There is hope, however, as Steve’s mix is 20% peanuts, while Grace’s is 70% peanuts. Carol should be able to combine some portion of their mixes to get what she needs. How much trail mix should she borrow from each of them in order to finish the hike?

Answer 1

Answer - 18 gms from Grace and 12 gms from Steve would give the 30 gms with 50% peanuts

Solution:

Say that Carol took x gms from Grace. Then she would take (30-x) gms from Steve

By solving 0.7(x) + 0.2 (30-x) = 0.5(30) for x, we would obtain x = 18 and thus the answer.