Question

8t+5h=220
5t+h=112

Answer 1

To solve the system of equations:

1. \( 8t + 5h = 220 \) (Equation 1)
2. \( 5t + h = 112 \) (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:
- \( t = 20 \)
- \( h = 12 \)