SOLUTION: Hank has some 60% maple syrup and some 100% maple syrup in his restaurant. How many ounces of EACH should he use to make 100 ounces of 85% maple syrup

Algebra ->  Percentages: Solvers, Trainers, Word Problems and pie charts -> SOLUTION: Hank has some 60% maple syrup and some 100% maple syrup in his restaurant. How many ounces of EACH should he use to make 100 ounces of 85% maple syrup      Log On


   

Question 566527: Hank has some 60% maple syrup and some 100% maple syrup in his restaurant. How many ounces of EACH should he use to make 100 ounces of 85% maple syrup
Found 2 solutions by josmiceli, Maths68:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = ounces of 60% m.s. needed
Let +b+ = ounces of 100% m.s. needed
given:
(1) +a+%2B+b+=+100+
(2) +%28.6a+%2B+1%2Ab%29+%2F+100+=+.85+
-------------------------
(2) +.6a+%2B+b+=+85+
(2) +6a+%2B+10b+=+850+
Multiply both sides of (1) by 6
and subtract (1) from (2)
(2) +6a+%2B+10b+=+850+
(1) +-6a+-+6b+=+600+
+4b+=+250+
+b+=+62.5+
and
(1) +a+%2B+62.5+=+100+
(1) +a+=+37.5+
37.5 ounces of 60% m.s. are needed
62.5 ounces of 100% m.s. are needed

Answer by Maths68(1474) About Me  (Show Source):
You can put this solution on YOUR website!
Solution A
Amount =x ounces
Concentration =60% = 0.6
Solution B
Amount = 100-x ounces
Concentration =100% = 1
Resultant Solution
Amount =100 ounces
Concentration =85%=0.85
[Amount Solution A * Concentration A] + [Amount Solution B * Concentration of B] = Amount of Resultant * Concentration of resultant
(x)(0.6)+(100-x)(1)=(100)(0.85)
0.6x+100-x=85
-0.4x=85-100
-0.4x=-15
-0.4x/-0.4=-15/-0.4
x=37.5



Solution A
Amount = x = 37.5 ounces
Concentration =60% = 0.6
Solution B
Amount = 100-x = 100-37.5 = 62.5 ounces
Concentration =100% = 1


Hank has to mix 37.5 ounces of 60% maple syrup and 62.5 ounces of 100% maple syrup to make 100 ounces of 85% maple syrup