Ascientist has two solutions, which she has labeled solution a and solution b. each contains salt. she knows that solution a is 60 % salt and solution b is 85 % salt. she wants to obtain 40 ounces of a mixture that is 65 % salt. how many ounces of each solution should she use?

answer:

32oz of a

8oz of b

step-by-step explanation:

model the problem with equations

let r be her desired solution in ounces

let a represent ounces of solution a

let b represent ounces of solution b

a + b = 40 = r

0.65r = 0.6a + 0.85b     =>   0.65(40) = 0.6a + 0.85b = 26

solve the system using substitution

a + b = 40

b = 40 - a

substitute b = 40 - a into 0.6a + 0.85b = 26

0.6a + 0.85b = 26

0.6a + 0.85(40 - a) = 26

0.6a + 34 - 0.85a = 26

isolate a

8 = 0.25a

a = 32

substitute a=32 into a + b = 40

a + b = 40

32 + b = 40

isolate b

b = 8

therefore, she needs to use 32 ounces of solution a and 8 ounces of solution b to get a 40 ounce mixture that is 65% salt.