A goldsmith combined an alloy that costs $4.50 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 $2.82 per ounce? $4.50 alloy oz $1.70 alloy oz

pobi1k

pobi1k

Answered question

2022-09-01

A goldsmith combined an alloy that costs $4.50 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 $2.82 per ounce?
$4.50 alloy oz
$1.70 alloy oz

Answer & Explanation

Yadira Mcdowell

Yadira Mcdowell

Beginner2022-09-02Added 13 answers

We have,
cost of 1 oz of 1 st alloy = $ 4.50
And, cost of 1 oz of 2nd alloy = $1.75
Let the weight of 1 st alloy in mixture =x oz
Then, the weight of 2nd alloy in mixture = ( 200 x ) o z
Now, according to question,
4.50 x + 1.70 x ( 200 x ) = 200 × 2.82 4.50 x + 340 1.70 x = 564 4.50 x 1.70 x = 564 340 2.80 x = 224 x = 224 2.80 = 80
1 st alloy = 80 oz
2nd alloy = (200-80)oz=120 oz
Hence, mixture contains 80 oz 1st alloy and 120 oz 2nd alloy.

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