the sum of two decimal numbers is 5.3. their difference is 1.7 and there product is 6.3 what are the two numbers?
x = one number
y = other number.
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x+y=5.3
x-y=1.7
Solve for x and y.
You don't need the other information but it can be used if you wish.
x+y = 5.3
x-y = 1.7
add them
2x = 7.0
x = 3.5
then y = 1.8
the info that their product is 6.3 was redundant, but checked out.
1.8 and 3.5. I just used guess and check. I knew that the numbers had to be under 5.3. Also, the number in the tenths place had to add up to 13 or 3, so 1.8 and 3.5.
To find the two decimal numbers, let's assign variables to represent the numbers.
Let's call the first number x, and the second number y.
We know three things about these numbers:
1. The sum of the two numbers is 5.3:
x + y = 5.3
2. The difference between the two numbers is 1.7:
x - y = 1.7
3. The product of the two numbers is 6.3:
x * y = 6.3
Now we have a system of three equations:
Equation 1: x + y = 5.3
Equation 2: x - y = 1.7
Equation 3: x * y = 6.3
We can use a method called substitution to solve this system of equations. Let's solve equation 2 for x:
x = 1.7 + y
Now substitute this value of x in equations 1 and 3:
Equation 1: (1.7 + y) + y = 5.3
Equation 3: (1.7 + y) * y = 6.3
Simplifying equation 1:
2.7 + 2y = 5.3
2y = 5.3 - 2.7
2y = 2.6
y = 2.6 / 2
y = 1.3
Now substitute the value of y back into equation 2:
x - 1.3 = 1.7
x = 1.7 + 1.3
x = 3
So the two numbers are x = 3 and y = 1.3.