MATH 121
MIXTURE PROBLEMS
In general: | fraction of the substance x amount of mixture = amount of the
substance.
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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!
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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?
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Alloy A: copper
Alloy B: copper Mixture: copper |
A B
Mixture |
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(24)+ x = (x + 24) |
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 |
121mix.hdt