Question 1078245
a goldsmith was going to make some rings out of his 1000 grams of gold <s>an</s> 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


{{{highlight_green(highlight_green(25x+50(1000-x)=1000*45))}}}
{{{25x+50000-50x=45000}}}
{{{25x-50x=45000-50000}}}
{{{-25x=-5000}}}
{{{25x=5000}}}
{{{highlight_green(x=200)}}}
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.




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