Respuesta :
Answer:
135.73 ounces of a silver alloy that costs $5.50 per ounce should be mixed.
Step-by-step explanation:
Given:
A silver alloy that costs $5.50 per ounce should be mixed with one that costs $7.00 per ounce to make a new 30 ounce alloy that costs $6.40 per ounce.
Now, to find the ounces of silver alloy.
Let the silver costs $5.50 per ounce be [tex]x.[/tex]
And the silver costs $7.00 per ounce be [tex]y.[/tex]
So, the total ounce make a new alloy:
[tex]x+y=30\\y=30-x[/tex] ....(1)
Now, the total costs of silver alloy:
[tex]5.50x+7y=6.4[/tex]
Putting the value of [tex]y[/tex] from equation (1) in the place of [tex]y[/tex] :
[tex]5.50x+7(30-x)=6.4[/tex]
[tex]5.50x+210-7x=6.4[/tex]
[tex]-1.5x+210=6.4[/tex]
Subtracting both sides by 210 we get:
[tex]-1.5x=-203.6[/tex]
Dividing both sides by -1.5 we get:
[tex]x=135.73[/tex]
Therefore, 135.73 ounces of a silver alloy that costs $5.50 per ounce should be mixed.
