Mixture Problems: silver alloy; acid soln; chocolate mix

[ysodimu]

Can someone please check if the below solutions are correct and if not tell me what I am doing wrong. Thanks in advance.

Question #1

How many ounces of a Silver Alloy that cost $6 per ounce must be mixed with
10 oz of Silver Alloy that cost $8 per ounce to make a mixture that cost $6.50 per ounces?

Solution: 6x + 8(10) = 6.50(10 + x)
6x + 80 = 65 + 6.50x
= 80 - 65 = 6.50x - 6x
= 15 = 0.5
= 15/0.5x = 0.5x/0.5x
x = 30

Question #2

How many gallons of a 15% acid solution must be mixed with 5 gal. of a 20% acid solution to make a 16% acid solution?

Solution: .15x + 1 = .16(16+x)
.15x + 1 = 2.56 + .16x
.15x - .16x = 2.56 - 1
-0.01x = 1.56
-0.01x/-0.01 = 1.56/-0.01x
x = -156

Question #3

How many ounces of pure chocolate must be added to 150 oz of chocolate topping that is 50% chocolate to make a topping that is 75% chocolate?

Solution: 75 = 0.75(150 + x)
75 = 112.5 + 0.75x
0.75x = 112.5 - 75
0.75x = 37.5
0.75x / 0.75x = 37.5 / 0.75x
x = 50

 

[ilaggoodly]

if you look at #3, 50% chocolate means you originally have 75 oz of chocolate. If you were to add 50 oz. you would have a solution of 125 oz. of chocolate and 200 oz. altogether ^^ which is not quite 75%
instead try something like this
\(\displaystyle \L 75%= \frac{50% \cdot (150) + x}{(150+x)}\)

 

[Denis]

#3 is quite obvious: x@50% + x@100% = 2x@75%

 

[ysodimu]

Which one of you is correct? does that mean that my equation and answer is wrong?

 

[stapel]

Which one of you is correct?

Each is correct. One provides you the equation to solve. The other points out that, for this specific percentage mix, there is a practical short-cut.

does that mean that my equation and answer is wrong?

Check your answer and find out:

If you add fifty ounces of 100%-chocolate topping (so fifty ounces of chocolate) to one hundred fifty ounces of 50%-chocolate topping (so seventy-five ounches of chocolate), you will get two hundred ounces of topping, containing one hundred twenty-five ounces of chocolate.

Is this a 75%-chocolate mix?

Eliz.