SOLUTION: Word problem: Translate the problem into a pair of linear equations in two vaiables. Solve the equations using either elimination or substitution. State your answer for the specif

Algebra ->  Coordinate Systems and Linear Equations -> SOLUTION: Word problem: Translate the problem into a pair of linear equations in two vaiables. Solve the equations using either elimination or substitution. State your answer for the specif      Log On


   



Question 310081: Word problem:
Translate the problem into a pair of linear equations in two vaiables. Solve the equations using either elimination or substitution. State your answer for the specified variable.
A garage owner wants to fill a 55-gallon drum with a 20% winter mixture of antifreeze for his customers. How many gallons of 100% antifreeze should he mix with some 10% antifreeze mixture in order to fill the drum?
I'm having difficulty writing equations from a word problem. Please show me the equations you created and steps to get to the answer. Please also show the answer. Thank you so much!

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let a = gallons of 100% antifreeze he needs
Let b = gallons of 10% antifreeze mixture he needs
given:
55 = gallons of mixture he ends up with
.2%2A55+=+11 = antifreeze in final mixture
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In words:
(total gallons of antifreeze in final mixture)/(total gallons of final mixture) = 20%
%28a+%2B+11%29%2F%28a+%2B+b%29+=+.2
a+%2B+b+=+55
Solve these equations for a and b.
Your answer will be a