Write an addition problem in which, when the addends are rounded to the nearest ten, the sum is 90. Then explain how you use estimation to solve the problem.

To create an addition problem in which the addends, when rounded to the nearest ten, sum up to 90, we can use estimation. Let's consider the following example:

Addend 1: 45 (rounded to the nearest ten would be 50)
Addend 2: 40 (rounded to the nearest ten would be 40)

To solve the problem using estimation, we round each addend to the nearest ten, add them up, and then check whether their sum is close to 90.

In this case, when we round 45 to the nearest ten, we get 50. When we round 40 to the nearest ten, it remains the same. Adding these rounded numbers together, 50 + 40 equals 90. Thus, even when rounding to the nearest ten, the sum still equals 90.

Therefore, using estimation allowed us to create an addition problem in which the addends, when rounded to the nearest ten, sum up to 90.

To create an addition problem that meets this criteria, let's assume the addends are x and y. We want the rounded sum to be 90, so we can set up the equation:

Round(x, -1) + Round(y, -1) = 90

Now, let's explore how to use estimation to solve the problem step-by-step:

Step 1: Round the number 90 to the nearest ten.
Rounded value: 90

Step 2: Choose two numbers, x and y, whose rounded values are close to 90.
Example: Let's choose x = 47 and y = 43.

Step 3: Round x to the nearest ten.
Rounded value of x: 50

Step 4: Round y to the nearest ten.
Rounded value of y: 40

Step 5: Add the rounded values of x and y.
50 + 40 = 90

Using estimation, we have found a valid addition problem where the addends, when rounded to the nearest ten, sum up to 90.