The sum of two decimal numbers is 5.3. Their differences is 1.7, and their product is 6.3. what are the two numbers?
qol-l:
x + y = 5.3
x - y = 1.7
So add the equations together:
2x = 7.0
x = 3.5
But x + y = 5.3, so
y = 1.8
Check it: x times y = 6.3. Correct!
To find the two numbers, let's assume one number as "x" and the other number as "y".
Given:
The sum of the two numbers is 5.3, which can be written as:
x + y = 5.3 --(1)
The difference between the two numbers is 1.7, which can be written as:
x - y = 1.7 --(2)
The product of the two numbers is 6.3, which can be written as:
x * y = 6.3 --(3)
Now, we have a system of three equations: Equation (1), Equation (2), and Equation (3). We can solve them simultaneously to find the values of x and y.
One way to solve this system of equations is through substitution:
From Equation (1), we can express x in terms of y:
x = 5.3 - y
Substitute this value of x in Equation (2):
(5.3 - y) - y = 1.7
Simplify:
5.3 - 2y = 1.7
Rearrange and solve for y:
-2y = 1.7 - 5.3
-2y = -3.6
y = (-3.6) / (-2)
y = 1.8
Now substitute the value of y in Equation (1) to find x:
x + 1.8 = 5.3
x = 5.3 - 1.8
x = 3.5
Therefore, the two numbers are 3.5 and 1.8.