The sum of two decimal numbers is 5.3. Their difference is 1.7, and their product is 6.3. What are the two numbers?

Does the product have anything to do with getting the answers?

You don't need the product info to solve this. You only need to write two equations to solve for two unknowns.

a + b = 5.3
a - b = 1.7

2a = 7
a = 3.5
b = 5.3 - 3.5 = 1.8

The product a*b does satisfy the 6.3 requirement. If it didn't, there would be no solution to all three requirements.

Thank you drwls!

I should not be using algebra for a sixth grade question. It's really the quickest way I know. I hope you were able to follow that.

Yes, the product of the two decimal numbers can help us find the values of the numbers. Let's go through the process of solving the problem step by step.

Let's assume the first decimal number is represented by x and the second decimal number is represented by y.

We are given three pieces of information:
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

To solve the problem, we can use a system of equations. We will solve the first equation for x and substitute it into the second equation to eliminate one of the variables. Then we can solve for y.

From the first equation, we can isolate x:
x = 5.3 - y

Substituting x into the second equation:
(5.3 - y) - y = 1.7
5.3 - 2y = 1.7

Simplifying the equation:
-2y = 1.7 - 5.3
-2y = -3.6
y = -3.6 / -2
y = 1.8

Now that we have the value of y, we can substitute it back into the first equation 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.