2 fractions have denominators 3 and 4. Their sum = 17/12. If the numerators are switched the sum = 3/2. Determine the 2 fractions.
Given:
x/3 + y/4 = 17/12
Common Denominator = 12:
4x/12 + 3y/12 = 17/12
4x + 3y = 17
Switch numerators:
y/3 + x/4 = 3/2
Common Denominator = 12:
4y/12 + 3x/12 = 3/2
3/2 = 18/12
So we have:
4y/12 + 3x/12 = 18/12
4y + 3x = 18
Our 2 simultaneous equations are:
4x + 3y = 17
3x + 4y = 18
Multiply equation 1 by 3 and equation 2 by 4
12x + 9y = 51
12x + 16y = 72
Subtract equation (2) - (1)
7y = 21
Divide each side by 7:
y = 3
Plug your = 3 into equation (2)
12x + 16(3) = 72
12x + 48 = 72
Subtract 48 from each side:
12x = 24
Divide each side by 12:
x = 2
The 2 fractions are:
2/3 and 3/4
Given:
x/3 + y/4 = 17/12
Common Denominator = 12:
4x/12 + 3y/12 = 17/12
4x + 3y = 17
Switch numerators:
y/3 + x/4 = 3/2
Common Denominator = 12:
4y/12 + 3x/12 = 3/2
3/2 = 18/12
So we have:
4y/12 + 3x/12 = 18/12
4y + 3x = 18
Our 2 simultaneous equations are:
4x + 3y = 17
3x + 4y = 18
Multiply equation 1 by 3 and equation 2 by 4
12x + 9y = 51
12x + 16y = 72
Subtract equation (2) - (1)
7y = 21
Divide each side by 7:
y = 3
Plug your = 3 into equation (2)
12x + 16(3) = 72
12x + 48 = 72
Subtract 48 from each side:
12x = 24
Divide each side by 12:
x = 2
The 2 fractions are:
2/3 and 3/4