How many quarts of pure antifreeze must be added to 8 quarts of a 20% antifreeze solution to obtain a 30% antifreeze solution? (Round to the nearest tenth as needed.)

9514 1404 393

  1.1 quarts

Step-by-step explanation:

Let x represent the amount to be added, in quarts. Then the amount of anti-freeze in the resulting solution is ...

  0.20(8) + 1.00(x) = 0.30(8 +x)

  0.70x = 0.10(8) . . . . . . subtract 0.20(8)+0.30(x)

  x = 8/7 . . . . . . . . . . . . . divide by the coefficient of x

  x ≈ 1.142857 ≈ 1.1

About 1.1 quarts of pure antifreeze must be added.

, and

for

step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote , , , so that we can call

note the following:

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from , to get to , we add

from , to get to , we add

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

, and for

ion

step-by-step explanation:

ion ion ion ion ion ion ion ion ion ion ion