when a fraction is reduced to its lowest term, it is equal to 3/4. The numerator of the fraction when doubled would be 34 greater than the denominator. Find the fraction.
N = Numerator
D = Denominator
Conditions :
N / D = 3 / 4
2 N = D + 34
N / D = 3 / 4 Multiply both sides by D
N = 3 D / 4
2 N = D + 34
2 * 3 D / 4 = D + 34
6 D / 4 = D + 34 Multiply both sides by 4
6 D = 4 D + 136 Subtract 4 D to both sides
6 D - 4 D = 4 D + 136 - 4 D
2 D = 136 Divide both sides by 2
D = 68
N = 3 D / 4
N = 3 * 68 / 4 = 204 / 4 = 51
51 / 68
Remark :
51 / 68 = 3 * 17 / ( 4 * 17 ) = 3 / 4
Thanks
4 reduced by D
8(2)-6=π100
In a class of 50 students,24 like football,21 basketball and 18 crickets.six like basketball and football only, 3 like basketball only 5 likes all games and 14 did not like any of the three.
I) illustrate this information on a Venn diagram
Ii)find the number of students who like
A) football and cricket only
B) exactly one games
To solve this problem, let's denote the numerator of the fraction as 'x' and the denominator as 'y'. We are given two pieces of information:
1) When the fraction is reduced to its lowest terms, it is equal to 3/4. This means that x/y = 3/4.
2) The numerator when doubled would be 34 greater than the denominator. Mathematically, this can be written as 2x = y + 34.
We can now solve these two equations simultaneously to find the values of x and y.
Step 1: Solve the first equation for x.
Multiply both sides of the equation x/y = 3/4 by y to eliminate the fraction:
x = (3/4) * y
Step 2: Substitute the value of x into the second equation.
Replace x in the equation 2x = y + 34 with (3/4) * y:
2 * ((3/4) * y) = y + 34
Step 3: Solve the equation for y.
Multiply both sides of the equation 2 * ((3/4) * y) = y + 34 by 4 to eliminate the fractions:
6y = 4(y + 34)
Distribute the 4 on the right side:
6y = 4y + 136
Subtract 4y from both sides:
6y - 4y = 136
2y = 136
Divide both sides by 2:
y = 68
Step 4: Find the value of x.
Substitute the value of y = 68 into the first equation x = (3/4) * y:
x = (3/4) * 68
x = 51
Therefore, the fraction is 51/68.