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.