SOLUTION: Write and solve a system of3. An embossing shop etches metal with acid solutions. The owner is discussing a certain job with the job supervisor, and they decide to use 30 ounces o

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Question 159180: Write and solve a system of3. An embossing shop etches metal with acid solutions. The owner is discussing a certain job with the job supervisor, and they decide to use 30 ounces of a 40% solution. Upon checking the acid solution supplies, the supervisor has found some 25% acid solution and some 50% acid solution, but there is no 40% acid solution. The owner explains to the supervisor how the two existing solutions can be mixed to obtain a 40% acid solution. How much of each solution is needed? equations for a given model / word problem:
Answer by ankor@dixie-net.com(12704) (Show Source):
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Write and solve a system of3. An embossing shop etches metal with acid solutions. The owner is discussing a certain job with the job supervisor, and they decide to use 30 ounces of a 40% solution. Upon checking the acid solution supplies, the supervisor has found some 25% acid solution and some 50% acid solution, but there is no 40% acid solution. The owner explains to the supervisor how the two existing solutions can be mixed to obtain a 40% acid solution. How much of each solution is needed? equations for a given model / word problem:
:
Let x = amt of 50% solution
It said the total has to be 30 oz, therefore:
(30-x) = 25% solution
:
Write a decimal equiv equation:
.50x + .25(30-x) = .40(30)
:
.50x + 7.5 - .25x = 12
;
.50x - .25x = 12 - 7.5
:
.25x = 4.5
x =
x = 18 oz of 50% solution
and
30 - 18 = 12 oz of 25% solution
;
:
Check solution in original equation:
.5(18) + .25(12) = .4(30)