Divide 75 into two parts so that twice the greater equals three times the smaller
g = the greater part
s = the smaller part
2 g = 3 s Divide both sides by 2
g = ( 3 / 2 ) s
g + s = 75
( 3 / 2 ) s + s = 75
( 3 / 2 ) s + ( 2 / 2 ) s = 75
( 5 / 2 ) s = 75 Multiply both sides by 2
5 s = 75 * 2
5 s = 150 Divide both sides by 5
s = 150 / 5
s = 30
g = ( 3 / 2 ) s
g = ( 3 / 2 ) * 30 = 3 * 30 / 2 = 90 / 2 = 45
the greater part = 45
the smaller part = 30
Proof:
Twice the greater equals three times the smaller.
2 * 45 = 3 * 30
90 = 90
To solve this problem, let's assume the two parts we need to find are "x" and "y".
According to the given information, we know that the sum of these two parts is 75:
x + y = 75
We are also told that twice the greater part (let's assume it is "x") is equal to three times the smaller part (which is "y"):
2x = 3y
Now, we can solve the system of equations consisting of these two equations:
From the first equation, we can express x in terms of y:
x = 75 - y
Substitute this value of x into the second equation:
2(75 - y) = 3y
Now, we can solve for y:
150 - 2y = 3y
Add 2y to both sides:
150 = 5y
Divide both sides by 5:
y = 30
Now, substitute the value of y back into the first equation to solve for x:
x + 30 = 75
Subtract 30 from both sides:
x = 45
Therefore, the two parts are 45 and 30.