Mixture Problems: dye solution; juice mix; silver alloy

[ysodimu]

More Solution to double check for me. I just want to make sure that I am on the right path and that my solution to the problems are accurate. thanks again for double checking my work.

Question #1

How many liters of a blue dye that costs $1.60 per liter must be mixed with 18L of Anil that cost $2.50 per liter to make a mixture that costs $1.90 per liter?

Solution: 1.60x + $45 = (18+x)(1.90)
1.60x + 45 = 34.20 + 1.90x
45-34.20 = 1.90x - 1.60x
10.8 = 0.3x
10.8/0.3x = 0.3x/0.3x
x = 36

Question #2

One hunderd ounces of juices that is 50% tomato juice are added to 200 oz of a vegetable juice that is 25% tomato juice. what is the percent concentration of tomato juice in the resulting mixure?

Solution: 50 + 200x = 75
200x = 75-50
200x = 25
200x/200x = 25/200x
x = 0.125 = 12.5%

Question # 3

Thirty ounces of pure Silver are added to 50 oz of Silver Alloy that is 20% Silver. what is the percent concentration of the resulting mixture?

Solution: 30x + 10 - 40

*I am not sure if my equation is correct, can someone please help me with this question #3? thanks.

 

[Deleted member 4993]

More Solution to double check for me. I just want to make sure that I am on the right path and that my solution to the problems are accurate. thanks again for double checking my work.

Question #1

How many liters of a blue dye that costs $1.60 per liter must be mixed with 18L of Anil that cost $2.50 per liter to make a mixture that costs $1.90 per liter?

Solution: 1.60x + $45 = (18+x)(1.90)
              1.60x + 45 = 34.20 + 1.90x
               45-34.20 = 1.90x - 1.60x
                10.8 = 0.3x
                 10.8/0.3x = 0.3x/0.3x
                 x = 36

Check
Cost of blue dye = 36 * 1.6 = 57.6
Cost of ANIL = 18 * 2.5 = 45
Cost of mixture = 102.6

Price of mixture = 54*1.9 = 102.6

Price = cost ........You are most probably correct

Now check the other problems similarly and tell us whether you right or wrong.

Question #2

One hunderd ounces of juices that is 50% tomato juice are added to 200 oz of a vegetable juice that is 25% tomato juice. what is the percent concentration of tomato juice in the resulting mixure?

Solution: 50 + 200x = 75
200x = 75-50
200x = 25
200x/200x = 25/200x
x = 0.125 = 12.5%

Question # 3

Thirty ounces of pure Silver are added to 50 oz of Silver Alloy that is 20% Silver. what is the percent concentration of the resulting mixture?

Solution: 30x + 10 - 40

*I am not sure if my equation is correct, can someone please help me with this question #3? thanks.

 

[Denis]

Just remember this:

a @ x
b @ y
=====
a+b@ z

z = (ax + by) / (a + b)