Ascientist has two solutions, which she has labeled solution a and solution b. each contains salt. she knows that solution a is 30% salt and solution b is 80% salt. she wants to obtain 50 ounces of a mixture that is 70% salt. how many ounces of each solution should she use? solution a= ? solution b= ? explain your steps.

10 ounces of solution a and 40 ounces of solution b.======let a be the volume of solution a, in ounces.let b be the volume solution b, in ounces.30% of solution a is salt. the decimal form of 30% is 0.3.  the volume of salt from solution a is    80% of solution b is salt. the decimal form of 80% is 0.8. the volume of salt from solution b is    the final mixture has total volume of 50 ounces, with 70% of it being salt. this means that the final  volume of salt is     0.7 × 50 ounces = 35 ouncesadding the volume of salt from solution a and the volume of  salt from solution b should get you the volume of salt in the final mixture. the salt does not come out of nowhere; it comes from the two added solutions. so    when we add two solutions together, the total volume of the final mixture is the sum of the volumes of the two solutions. adding the volumes of each solution should get a total of 50 ounces.again, solution does not magically come out of nowhere; it comes from the two added solutions. so then    therefore, we have this system of equations to solve:     we can solve this by substitution.if we rearrange equation (ii), we can isolate a.    we can substitute this for a in equation (i).    distribute 0.3    0.8b and -0.3b are like terms; combining them gives us 0.5b    use equation (i) to get the value of a.    so 10 ounces of solution a and 40 ounces of solution b.

31 is prime. and it’s prime factorization is just 31.

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