Divide 75 into 2 parts so that 3 times one part exceeds twice the other part by 5.
44,31
Just stating the answer is not helping Tourille learning how to do this.
seperate 39 into 2 parts with one number 5 more than the other
To solve this problem, we will set up two equations based on the given information.
Let's assume one part is represented by 'x', and the other part is represented by 'y'.
According to the problem:
1) "Divide 75 into 2 parts" means: x + y = 75
2) "3 times one part exceeds twice the other part by 5" can be translated to: 3x = 2y + 5
Now, we have a system of two equations:
Equation 1: x + y = 75
Equation 2: 3x = 2y + 5
To solve this system of equations, we will use substitution or elimination methods.
Method 1: Substitution
1) Solve Equation 1 for x:
x = 75 - y
2) Substitute the expression for x in Equation 2:
3(75 - y) = 2y + 5
3) Simplify the equation by using the distributive property:
225 - 3y = 2y + 5
4) Rearrange the equation, grouping like terms:
5y = 220
5) Solve for y by dividing both sides of the equation by 5:
y = 44
6) Substitute the value of y back into Equation 1 to find x:
x + 44 = 75
x = 75 - 44
x = 31
So, the two parts are 31 and 44, respectively.
Method 2: Elimination
1) Multiply Equation 1 by 2 to eliminate x:
2(x + y) = 2(75)
2x + 2y = 150
2) Rearrange Equation 2 to bring it in the form of 2x + 2y:
3x - 2y = 5
3) Multiply Equation 2 by 2 to eliminate y:
2(3x - 2y) = 2(5)
6x - 4y = 10
4) Subtract the equation obtained in step 3 from equation obtained in step 1:
(2x + 2y) - (6x - 4y) = 150 - 10
2x + 2y - 6x + 4y = 140
-4x + 6y = 140
5) Multiply the equation obtained in step 2 by 3 to make the coefficients of x equal:
3(3x - 2y) = 3(5)
9x - 6y = 15
6) Add the equation obtained in step 5 to equation obtained in step 4:
-4x + 6y + 9x - 6y = 140 + 15
5x = 155
7) Solve for x by dividing both sides of the equation by 5:
x = 31
8) Substitute the value of x back into Equation 1 to find y:
31 + y = 75
y = 75 - 31
y = 44
Both methods give us the same answer: x = 31 and y = 44, which are the two parts that divide 75 as required.