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A goldsmith combined an alloy that costs $4.20 per ounce with an alloy that costs $1.70 per ounce. How many ounces of each were used to make a mixture of 200 oz costing $2.25 per ounce?

Sagot :

Avril1938
so your finding an average so you already know the alloy that cost 1.70 that there will be more of that 

1.60      150     240    
4.20       50      210                  this your answer 150 of the 1.60 and 50 of the 4.20 this adds up to be 450/200 which equals 2.25

Answer:

For $4.20 we required 44 ounces.

For $1.70 we require 156 ounces.

Step-by-step explanation:

Given : A goldsmith combined an alloy that costs $4.20 per ounce with an alloy that costs $1.70 per ounce.

To find : How many ounces of each were used to make a mixture of 200 oz costing $2.25 per ounce?

Solution :

Let x be the amount of $4.20 per ounce.

A mixture of total is 200 oz.

So, 200-x is the amount of $1.70 per ounce.

According to question,

The equation form is [tex]4.20\times x+1.70\times (200-x)=2.25\times 200[/tex]

Solve the equation,

[tex]4.20x+340-1.70x=450[/tex]

[tex]2.5x+340=450[/tex]

[tex]2.5x=450-340[/tex]

[tex]2.5x=110[/tex]

[tex]x=\frac{110}{2.5}[/tex]

[tex]x=44[/tex]

So, For $4.20 we required 44 ounces.

For $1.70 we require 200-44=156 ounces.

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