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Substitution Word Problem

Shelby and Calvin need 5 ounces of a solution that is 65% acid and 35% distilled water.  They have 2 flasks of diluted acid: Flask A contains 70% acid and 30% distilled water, Flask B contains 20% acid and 80% distilled water. 

Write a system of equations that they can use to determine how many ounces they need to pour into each flask to make their solution, and solve the equations to determine how many ounces from each flask they need.

 

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1 Answer

A = amount from flask A

B = amount from flask B

A+B = 5 ......(1)

.7A+.2B = .65*5 ......(2)

5*(2) - (1): 2.5A = 11.25

A = 4.5 oz

B = 0.5 oz

Answer: You need 4.5 oz from flask A and 0.5 oz from flask B to make 5 oz of a solution that is 65% acid and 35% distilled water.

Comments

If you have to use substitution, solve B from (1), B = 5-A, and substitute it in (2) to get,

.7A+.2(5-A) = .65*5

A = 4.5 oz

B = 5-A = 0.5 oz

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