Divide 60 into 2 parts, such that twice the smaller number exceeds half of the greater number by 10
x and (60-x)
2 x -.5(60-x) = 10
2 x -30 +.5 x = 10
2.5 x = 40
25 x =400
x = 16
60-x = 44
Let's assume the smaller number is represented by 'x' and the greater number is represented by 'y'.
According to the given condition, twice the smaller number exceeds half of the greater number by 10. Mathematically, this can be represented as:
2x = (y/2) + 10
To solve this problem, we can set up a system of equations based on the information given.
Equation 1: x + y = 60 (since we are dividing 60 into 2 parts)
Equation 2: 2x = (y/2) + 10
First, let's solve Equation 2 for x:
2x = (y/2) + 10
Multiply both sides by 2 to eliminate the denominator:
4x = y + 20
Now we have two equations:
Equation 1: x + y = 60
Equation 3: 4x = y + 20
To solve this system of equations, we can use substitution. Rearrange Equation 1 to solve for x:
x = 60 - y
Now substitute this expression for x in Equation 3:
4(60 - y) = y + 20
Simplify the equation:
240 - 4y = y + 20
Combine like terms:
240 - 20 = y + 4y
220 = 5y
Divide both sides by 5:
44 = y
Now substitute this value for y in Equation 1 to find x:
x + 44 = 60
x = 60 - 44
x = 16
Therefore, the two numbers are 16 and 44, which sum up to 60 and satisfy the condition that twice the smaller number exceeds half of the greater number by 10.
To solve this problem, let's assume that the smaller number is represented by 'x' and the greater number is represented by 'y'.
According to the given condition, "twice the smaller number exceeds half of the greater number by 10," we can create an equation:
2x = (1/2)y + 10
Now, we have one equation and two variables. To solve for 'x' and 'y', we need another equation. The other equation would come from the fact that we are trying to divide 60 into two parts. So we can also say:
x + y = 60
Now we have a system of equations:
2x = (1/2)y + 10
x + y = 60
We can solve this system of equations using various methods like substitution or elimination. Let's use substitution:
1. Solve the second equation for 'x':
x = 60 - y
2. Substitute the value of 'x' in the first equation:
2(60 - y) = (1/2)y + 10
3. Simplify and solve for 'y':
120 - 2y = (1/2)y + 10
120 - 10 = (1/2)y + 2y
110 = (5/2)y
4. Solve for 'y':
y = 110 * (2/5) = 44
5. Substitute the value of 'y' back into the second equation to solve for 'x':
x + 44 = 60
x = 60 - 44 = 16
Therefore, the two parts of 60 that satisfy the given condition are 16 and 44.