SOLUTION: 1. How many oz. of pure nickel must be added to 150 oz. of alloy 70% pure to make an alloy which is 85% pure? 2. How much water must be added to 200 gallons of mixture which is 80

Question 623192: 1. How many oz. of pure nickel must be added to 150 oz. of alloy 70% pure to make an alloy which is 85% pure?
2. How much water must be added to 200 gallons of mixture which is 80% alcohol to reduce it to a 75% mixture?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
1. How many oz. of pure nickel must be added to 150 oz. of alloy 70% pure to make an alloy which is 85% pure?

let x = the amount of nickel to be added to the mixture.
your formula will be:
.7*150 + x = .85(150 + x)
simplify this to get:
.7*150 + x = .85*150 + .85*x
subtract .85*x from both sides of this equation to get:
.7*150 + .15*x = .85*150
subtract .7*150 from both sides of this equation to get:
.15*x = .85*150 - .7*150
simplify to get:
.15*x = 22.5
divide both sides of this equation by .15 to get:
x = 22.5 / .15 = 150
this means you need to add 150 ounces of nickel to the mixture to get an allow that's 85% nickel.
150 + 150 = 300 ounces in the new mixture.
the amount of nickel in the new mixture is equal to:
.7 * 150 + 150 = 105 + 150 = 255 ounces of nickel in the next mixture.
the percent nickel in the new mixture is 255 / 300 = .85 = 85%.

2. How much water must be added to 200 gallons of mixture which is 80% alcohol to reduce it to a 75% mixture?

this one's trickier.
.8 * 200 equals amount of alcohol in the original mixture.
this means that .2 * 200 equals the amount of water in the original mixture.
you want to add water to make the amount of alcohol equal to .75 of the next mixture.
this means you want to have water equal to .25 of the new mixture.
your formula is:
.20*200 + x = .25 * (200 + x)
simplify this to get:
40 + x = 50 + .25*x
subtract .25*x from both sides of the equation and subtract 40 from both sides of the equation to get:
x - .25*x = 50 40 which results in:
.75*x = 10
divide both sides of the equation by .75 to get:
x = 10 / .75 which is equal to 13.333333 or 40/3.
you will need to add 40/3 gallons of water to the original mixture.
you will get:
amount of alcohol in the original mixture is .8 * 200 = 160 gallons.
this is the amount of gallons of alcohol that be in the new mixture because you didn't add any alcohol.
you add 40/3 gallons of water to the original mixture to get a total mixture of 200 + 40/3 = 600/3 + 40/3 = 640/3 gallons in the new mixture (equivalent to 213.333333 gallons).
160 gallons of alcohol in the new mixture divided by 640/3 gallons of total mixture is equivalent to 160 * 3 / 640 which is equivalent to 480 / 640 which is equivalent to 48 / 64 which is equivalent to 3/4 which equals 75%.
you needed to convert the problem to amount of water so you can add water and you're dealing with the same quantities in the equation. you have water in the original mixture and you add water to make the amount of water in the new mixture.

RELATED QUESTIONS
How many ounces of pure silver must be added to 36 OZ of 60% pure silver to make an alloy (answered by richwmiller)

how many ounces of pure nickel must be added to 150 ounces of an allot which is 85%... (answered by josmiceli)

How many oz. of pure chocolate must be added to 150 oz that is 60% chocolate to make a... (answered by venugopalramana)

In order for a metal to be labeled "A," the silver alloy must contain at least % of pure... (answered by ikleyn)

how many ounces of pure silver that cost $8.50 an ounce must be mixed with 100 oz of a... (answered by josgarithmetic)

One bar of tin alloy is 25% pure tin and another bar is 10% pure tin. How many pounds of... (answered by fractalier)

A goldsmith combined pure gold that cost $400 per ounce with an alloy of gold that costs... (answered by rfer)

How many grams of pure gold must be added to 200g of 25% gold alloy to make an alloy of... (answered by josgarithmetic)

How many 6 mg of mg of a metal containing 45% nickel must be combined with 6 mg of pure... (answered by checkley77)