Find the Standard Form 0.1x+0.4y=0.25(100)

Math
0.1x+0.4y=0.25(100)
The standard form of a linear equation is Ax+By=C.
Change 0.1 into a fraction.
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Multiply by 1010 to remove the decimal.
10⋅0.110x+0.4y=0.25(100)
Multiply 10 by 0.1.
110x+0.4y=0.25(100)
Cancel the common factor of 1 and 10.
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Rewrite 1 as 1(1).
1(1)10x+0.4y=0.25(100)
Cancel the common factors.
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Rewrite 10 as 1(10).
1⋅11⋅10x+0.4y=0.25(100)
Cancel the common factor.
1⋅11⋅10x+0.4y=0.25(100)
Rewrite the expression.
110x+0.4y=0.25(100)
110x+0.4y=0.25(100)
110x+0.4y=0.25(100)
110x+0.4y=0.25(100)
Change 0.4 into a fraction.
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Multiply by 1010 to remove the decimal.
110x+10⋅0.410y=0.25(100)
Multiply 10 by 0.4.
110x+410y=0.25(100)
Cancel the common factor of 4 and 10.
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Factor 2 out of 4.
110x+2(2)10y=0.25(100)
Cancel the common factors.
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Factor 2 out of 10.
110x+2⋅22⋅5y=0.25(100)
Cancel the common factor.
110x+2⋅22⋅5y=0.25(100)
Rewrite the expression.
110x+25y=0.25(100)
110x+25y=0.25(100)
110x+25y=0.25(100)
110x+25y=0.25(100)
Change 0.25 into a fraction.
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Multiply by 100100 to remove the decimal.
110x+25y=100⋅0.25100⋅100
Multiply 100 by 0.25.
110x+25y=25100⋅100
Cancel the common factor of 25 and 100.
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Factor 25 out of 25.
110x+25y=25(1)100⋅100
Cancel the common factors.
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Factor 25 out of 100.
110x+25y=25⋅125⋅4⋅100
Cancel the common factor.
110x+25y=25⋅125⋅4⋅100
Rewrite the expression.
110x+25y=14⋅100
110x+25y=14⋅100
110x+25y=14⋅100
110x+25y=14⋅100
Find the LCD of 110, 25, and 14.
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Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.
10,5,4
Since 10,5,4 contain both numbers and variables, there are two steps to find the LCM. Find LCM for the numeric part 10,5,4 then find LCM for the variable part .
The LCM is the smallest positive number that all of the numbers divide into evenly.
1. List the prime factors of each number.
2. Multiply each factor the greatest number of times it occurs in either number.
10 has factors of 2 and 5.
2⋅5
Since 5 has no factors besides 1 and 5.
5 is a prime number
4 has factors of 2 and 2.
2⋅2
The LCM of 10,5,4 is the result of multiplying all prime factors the greatest number of times they occur in either number.
2⋅2⋅5
The LCM of 10,5,4 is 2⋅2⋅5=20.
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Multiply 2 by 2.
4⋅5
Multiply 4 by 5.
20
20
20
Multiply both sides by 20.
20(110x+25y)=20(14⋅100)
Simplify 20(110x+25y).
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Simplify each term.
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Combine 110 and x.
20(x10+25y)=20(14⋅100)
Combine 25 and y.
20(x10+2y5)=20(14⋅100)
20(x10+2y5)=20(14⋅100)
Simplify terms.
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Apply the distributive property.
20×10+202y5=20(14⋅100)
Cancel the common factor of 10.
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Factor 10 out of 20.
10(2)x10+202y5=20(14⋅100)
Cancel the common factor.
10⋅2×10+202y5=20(14⋅100)
Rewrite the expression.
2x+202y5=20(14⋅100)
2x+202y5=20(14⋅100)
Cancel the common factor of 5.
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Factor 5 out of 20.
2x+5(4)2y5=20(14⋅100)
Cancel the common factor.
2x+5⋅42y5=20(14⋅100)
Rewrite the expression.
2x+4(2y)=20(14⋅100)
2x+4(2y)=20(14⋅100)
Multiply 2 by 4.
2x+8y=20(14⋅100)
2x+8y=20(14⋅100)
2x+8y=20(14⋅100)
Simplify 20(14⋅100).
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Cancel the common factor of 4.
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Factor 4 out of 100.
2x+8y=20(14⋅(4(25)))
Cancel the common factor.
2x+8y=20(14⋅(4⋅25))
Rewrite the expression.
2x+8y=20⋅25
2x+8y=20⋅25
Multiply 20 by 25.
2x+8y=500
2x+8y=500
Find the Standard Form 0.1x+0.4y=0.25(100)

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