Question

A chemist has 100 g of a 15% saline solution that she wants to strengthen to 29%. The percentage P of salt in the solution by mass can be modeled by P(x) =

100(15 + x)/
100 + x
, where x is the number of grams of salt added.

Part 1 out of 2
Select the graph of the function for 0 ≤ x ≤ 100.

Answer 1

D., x= 19.7 or ≈20. g

Explanation:

P(x) = [100(15+x)]/(100+x)

When 0 g additional salt is added, x=0. we have

P(0) = [100(15+0)]/(100+0)= 15

x=0, P=15

We can see this point only on the graph D.

P(x) =29 = [100(15+x)]/(100+x)

29 = [100(15+x)]/(100+x)

29(100+x) = 100(15+x)

2900+29x = 1500+100x

2900-1500=100x-29x

1400 = 71x

x ≈ 19.7 g or ≈20. g

From the graph D, we can see that to get 29% we need to add ≈ 20 g of salt.