A scientist has two solutions, which she has labeled soultion A and solution B.

Question

A scientist has two solutions, which she has labeled soultion A and solution B. Each cintains salt. She knows that solution A is 60% salt and solution B is 90% salt. She wants to obtain 120 ounces of a mixture that is 80% salt. How many ounces of each solution should she use ? A scientist has two solutions, which she has labeled soultion A and solution B. Each cintains salt. She knows that solution A is 60% salt and solution B is 90% salt. She wants to obtain 120 ounces of a mixture that is 80% salt. How many ounces of each solution should she use ?

Explanation / Answer

Let x ounces of solution A and y ounces of solution B be mixed to obtain 120 ounces of a mixture that is 80% salt. Then, we have x +y = 120…(1) ( as the total volume of the mixture is 120 ounces). Also x*60/100+ y*90/100 = 120*80/100 or, 60x +90y = 9600 . On dividing both the sides by 30, we get 2x+3y= 320…(2). On multiplying both the sides of the 1st equation by 2, we get 2x+2y = 240…(3). Now, on subtracting the 3rd equation from the 2nd equation, we get 2x+3y -2x-2y = 320-240 or, y =80. Then, from the 1st equation, we get x = 120 –y = 120-80 = 49. Thus, 40 ounces of solution A and 80 ounces of solution B have to be mixed to obtain 120 ounces of a mixture that is 80% salt.

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