To solve the system of equations:
- \( 8t + 5h = 220 \) (Equation 1)
- \( 5t + h = 112 \) (Equation 2)
We can use substitution or elimination. Here, we will use the substitution method.
First, solve Equation 2 for \( h \):
\[ h = 112 - 5t \]
Now substitute this expression for \( h \) into Equation 1:
\[ 8t + 5(112 - 5t) = 220 \]
Distribute \( 5 \):
\[ 8t + 560 - 25t = 220 \]
Combine like terms:
\[ -17t + 560 = 220 \]
Now isolate \( t \):
\[ -17t = 220 - 560 \] \[ -17t = -340 \] \[ t = \frac{-340}{-17} = 20 \]
Now that we have \( t \), substitute it back into the expression for \( h \):
\[ h = 112 - 5(20) \] \[ h = 112 - 100 = 12 \]
Thus, the solution to the system of equations is:
\[ t = 20, \quad h = 12 \]
In conclusion:
- \( t = 20 \)
- \( h = 12 \)