SOLUTION: I am having trouble setting up the equations for the following problem: a goldsmith was going to make some rings out of his 1000 grams of gold an alloy which would contain 45% g

Question 1078245: I am having trouble setting up the equations for the following problem:
a goldsmith was going to make some rings out of his 1000 grams of gold an alloy which would contain 45% gold. The goldsmith was going to use 2 different types of alloys and melt them together. One of the alloys was 25% AND THE OTHER 50% GOLD. How many grams of each type would the goldsmith have to use?
I have .25x+.50y=450 so far, but I need one more equation to solve using elimination. please help
Answer by josgarithmetic(39617) (Show Source): You can put this solution on YOUR website!
a goldsmith was going to make some rings out of his 1000 grams of gold an alloy which would contain 45% gold. The goldsmith was going to use 2 different types of alloys and melt them together. One of the alloys was 25% AND THE OTHER 50% GOLD. How many grams of each type would the goldsmith have to use?

x, how much of the 25% gold alloy to use
1000-x, how much of the 50% gold alloy to use

You really need just one variable and one equation. Solve this one here for x, and that will be how many grams of the 25% alloy to use. Computing then 1000-x is simple to do for the 50% alloy.

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You could still setup for two equations in two unknowns.
https://www.algebra.com/my/Mixtures%3A-All-in-Symbols.lesson?content_action=show_dev
https://www.algebra.com/my/Mixtures%3A-All-in-Symbols.lesson?content_action=show_dev
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