SOLUTION: half of the sum of two numbers is 6 less than the first number.one-third of their difference is one less than the second number. Find the numbers
Algebra.Com
Question 649437: half of the sum of two numbers is 6 less than the first number.one-third of their difference is one less than the second number. Find the numbers
Answer by shweta(56) (Show Source): You can put this solution on YOUR website!
Let the two numbers be x and y
Half of the sum of the numbers= {1*(x+y)}/2=(x+y)/2
(x+y)/2=x-6 .......(1)
One-third of their difference={1*(x-y)}/3=(x-y)/3
(x-y)/3=y-1 ........(2)
x-y=3*(y-1)
x-y=3y-3
x-y-3y=-3
x-4y=-3 ........(3)
Now consider equation (1)
(x+y)=2*(x-6) (on cross multiplication)
x+y=2x-12
x-2x+y=-12
-x+y=-12 .......(4)
Now we have got two linear equations .
x-4y=-3
-x+ y=-12
we need to find the value of each variable .We will start by cancelling one variable so that we can get the value of other variable
Add the above equation, we get
-4y+y=-3-12 (x-x=0)
-3y= -15
Negative sign on both the sides get cancelled
3y=15
y=15/3
y= 5
Now substitute the value of y in equation(4)
y-x=-12
5-x=-12
-x= -12-5
-x=-17
x=17
RELATED QUESTIONS
The sum of two numbers is 6 less than twice the first number.
Their difference is 10... (answered by awang1996)
The sum of two numbers is 23 less than twice the first number. Their difference is 19... (answered by dfrazzetto)
The sum of two numbers is 54. One fourth of the first number is three less than half the... (answered by user_dude2008)
The sum of two numbers is 15 less than twice the first number. Their difference is 5 less (answered by Paul)
The sum of two numbers is 13 more than twice the first number. Their difference is 14... (answered by josgarithmetic,MathTherapy)
The sum of two numbers is 6 less than twice the first number. Their difference is 10 less (answered by ankor@dixie-net.com)
One number is 15 less than half of another number, their sum is 6 what are the other... (answered by ewatrrr)
the sum of 2 numbers is 15 less than twice the first number. their difference is 5 less... (answered by RAY100)
The sum of two numbers is 6 less than twice the first number. Their difference is 10... (answered by ankor@dixie-net.com)