SOLUTION: Write a linear equation to model this situation. An alloy is a mixture of metals. An artist was commissioned to make a 100g bracelet with a 50% silver alloy. He has a 60% silver

Question 388140: Write a linear equation to model this situation. An alloy is a mixture of metals. An artist was commissioned to make a 100g bracelet with a 50% silver alloy. He has a 60% silver alloy and a 35% silver alloy.
Solve this using elimination or substitution.
Help!
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
bracelet will be 100 grams with a 50% silver alloy.
artist has 60% silver alloy and 35% silver alloy.
he needs to combine these together to make the bracelet with 50% silver alloy.

x = number of grams of 60% silver alloy.
y = number of grams of 35% silver alloy.

x + y = 100 grams of bracelet

.60 * x = amount of silver in the first alloy.
.35 * y = amount of silver in the second alloy.

.60 * x + .35 * y = .50 * 100 grams of silver in the bracelet

your 2 equations that you need to solve simultaneously are:

x + y = 100

.60*x + .35*y = .50*100

we'll use substitution.

from the first equation, solve for y to get y = 100 - x

substitute 100-x for y in the second equation to get:

.60*x + .35*(100-x) = .5*100
simplify to get:
.60*x + .35*100 - .35*x = .5*100
simplify to get:
.60*x + 35 - .35*x = 50
combine like terms to get:
.25*x + 35 = 50
subtract 35 from both sides to get:
.25*x = 50-35
simplify to get:
.25*x = 15
divide both sides by .30 to get:
x = 15/.25 = 60
if x = 60, then y = 100 - 60 = 40

you need 60 grams of 60% alloy and 40 grams of 35% alloy.

60 + 40 = 100 grams of alloy in the bracelet (from x + y = 100).

.6*60 + .35*40 = 36 + 14 = 50 grams of silver in the bracelet (from .6*x + .25*y = .5*100).

Your answer is:

He needs 60 grams of 60% alloy and 40 grams of 35% alloy to make the bracelet.

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