MATH 121
MIXTURE PROBLEMS

 

In general: fraction of the substance x amount of mixture = amount of the substance.

 

Example 1: How many gallons of a 12% solution should be combined with 10 gallons of an 18% solution to obtain a 16% solution?

(sum of parts = whole!)

12x + 18(10) = 16(x + 10) can forget % since in all terms!
6x + 90 = 8(x + 10)
6x + 90 = 8x + 80
-2x = -10
x = 5                  5 gallons

 

Example 2:

Alloy A is 1 part copper to 3 parts tin. Alloy B is 1 part copper to 4 parts tin. How much of alloy B should be added to 24 pounds of alloy A to obtain an alloy that is 2 parts copper to 7 parts tin?

 

Alloy A: copper     
Alloy B: copper
Mixture: copper
   A       B       Mixture
 

(24)+ x = (x + 24)
6 + x = (x + 24)
270 + 9x = 10(x + 24)
270 + 9x = 10x + 240
30 = x                30 lb.

1) How many gallons of a 20% salt solution must be combined with 18 gallons of a 28% salt solution to obtain a 22% solution?

2) How much pure acid should be added to 5 gallons of 40% acid solution to obtain a 50% acid solution?

3) A martini mix contains 4 parts gin to 1 part vermouth. A drier mix contains 6 parts gin to 1 part vermouth. How much of the drier mix must be used for 15 ounces of mixture that is 5 parts gin to 1 part vermouth?

4) How much cream that contains 33% butterfat must be blended with milk that contains 3% butterfat to obtain 10 gallons of half and half that contains 8% butterfat?

5) Ten gallons of chocolate ice cream that contains 18% butterfat is mixed with 8 gallons of vanilla ice cream that contains 12% butterfat to make chocolate ripple ice cream. What percent butterfat does the chocolate ripple contain?

6) A grocer mixes 6 pounds of coffee that is 60% Columbian with one that is 80% Columbian. How much of the second type should be used to obtain a mixture that is 78% Columbian?

7) Twenty gallons of milk containing 4 percent butterfat is mixed with 16 gallons of milk containing 6 percent butterfat. How many gallons of skim milk having percent butterfat should be added to obtain milk containing 4 percent butterfat?

8) An automobile radiator contains 8 gallons of a solution that is 10% antifreeze and 90% water. How much of the solution must be drained and replaced with pure antifreeze in order to obtain a solution that is 25% antifreeze?

9) How many ounces of an alloy containing 60% silver must be added to 50 pounds of an alloy containing 45% silver to obtain an alloy containing 51% silver?

 

ANSWERS:

1) 54 gallons

2) 1 gallon

3) 8 ounces

4)gallons or 1 gallons

5) % or 15%

6) 54 pounds

7) gallons or 3 gallons

8) gallons or 1 gallons

9) ounces or 33 ounces

 

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