Question

___10
900+___+ 6+200+80+70
___+200+____+3
= 1,243

Answer 1

To solve for the missing values in the equation below, we need to express it as an equation and find the appropriate numbers.

The equation we have is:

\[
900 + x + 6 + 200 + 80 + 70 + y + 200 + z + 3 = 1,243
\]

First, let's simplify the equation by adding the constant values:

\[
900 + 6 + 200 + 80 + 70 + 200 + 3 = 1,459
\]

So, we compute the sum of known values:

\[
900 + 6 = 906 \\
906 + 200 = 1,106 \\
1,106 + 80 = 1,186 \\
1,186 + 70 = 1,256 \\
1,256 + 200 = 1,456 \\
1,456 + 3 = 1,459
\]

Now let's substitute this back into the equation:

\[
x + y + z + 1,459 = 1,243
\]

Now let's isolate \(x + y + z\):

\[
x + y + z = 1,243 - 1,459 = -216
\]

To maintain the integrity of the equation, \(x\), \(y\), and \(z\) must be chosen such that their sum equals -216. This means at least one of the variables must be negative, as they cannot all be positive.

One potential solution could be:

- Let \(x = -200\)
- Let \(y = -16\)
- Let \(z = 0\)

In this case:

\[
-200 + -16 + 0 = -216
\]

This gives a valid equation that balances out to 1,243 when added to the sum of constants.

Thus, the values are:
- \(x = -200\)
- \(y = -16\)
- \(z = 0\)

Verifying the calculation:

\[
900 + (-200) + 6 + 200 + 80 + 70 + (-16) + 200 + 0 + 3 = 1,243
\]

This indeed satisfies the equation.