The sum of two numbers is 119 and their difference is 29. what are the numbers?
Answers
Step-by-step explanation:
we have 2 different equations using the same variables, x and y:
x + y = 119
x - y = 15
We have the option of now rewriting one of the above equations in terms of either x or y
In this case, it seems easier to solve the second one for x, giving us x = 15 + y
Substituting that in for x in the first equation gives us (15 + y) + y = 119 or 2y + 15 = 119
Solving for y gives us y = 52 (by subtracting 15 from both sides and then dividing both sides by 2)
We can then use the fact that y = 52 and substitute it into one of the equations to get x. Sticking with the second equation, we have x - 52 = 15
Adding 52 to 15 gives us x = 67
That means our final answer is: x = 67 and y = 52
Checking our work gives us the following:
67 +52 = 119
67 - 52 = 15
Answer:
We know that the arithmetic mean between two numbers a and b is AM=
2
a+b
.
Here, it is given that AM=12, therefore,
AM=
2
a+b
⇒12=
2
a+b
⇒a+b=12×2
⇒a+b=24....(1)
It is also given that the product of two numbers a and b is 119, thus,
ab=119.....(2)
Now using equations 1 and 2, consider,
(a−b)
2
=(a+b)
2
−4ab=(24)
2
−(4×119)=576−476=100 implies that
a−b=10.....(3)
Adding equations 1 and 3, we have
(a+a)+(b−b)=24+10
⇒2a=34
⇒a=
2
34
=17
Substitute the value of a in equation 1 as follows:
17+b=24
b=24−17=7
Hence, the numbers are 17 and 7.
I hope it help you...