Equations of Exponential Functions
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Answer:
18 kilograms of 30% copper alloy is mixed with 72 kilograms of 55% copper alloy to makes 90 kg of a 50% copper alloy .
Step-by-step explanation:
Let us assume that the kilogram of 30% copper used to make alloy be x .
Let us assume that the kilogram of 55% copper used to make alloy be y .
As given
A metalworker has a metal alloy that is 30% copper and another alloy that is 55% copper.
The metalworker combine to create 90 kg of a 50% copper alloy .
Equation becomes
x + y = 90
30% is written in the decimal form .
= 0.30
55% is written in the decimal form .
= 0.55
50% is written in the decimal form .
= 0.50
Equation becomes
Concentration of 30% copper alloy × Number of kilograms of 30% copper alloy used + Concentration of 55% copper alloy × Number of kilograms of 55% copper alloy used = Concentration of 50% copper alloy × Number of kilograms of 50% copper alloy .
0.30x + 0.55y = 0.50 × 90
Simplify the above equation
30x + 55y = 4500
Two equation becomes
x + y = 90
30x + 55y = 4500
Multiply x + y = 90 by 30 and subtracted form 30x + 55y = 4500 .
30x - 30x + 55y - 30y = 4500 - 2700
25y = 1800
y = 72 kilograms
Putting the value of y in the equation .
x + 72 = 90
x = 90 - 72
x = 18 kilograms
Therefore 18 kilograms of 30% copper alloy is mixed with 72 kilograms of 55% copper alloy to makes 90 kg of a 50% copper alloy .