Question

Equation: w=112+8t

(2 points)
Which input results in an output of 176?

What is the output in the ordered pair (4, 144)?

Answer 1

To solve for the input that results in an output of 176, we can set up the equation based on the given formula \( w = 112 + 8t \).

1. **Finding \( t \) for \( w = 176 \)**:
\[
176 = 112 + 8t
\]
Subtract 112 from both sides:
\[
176 - 112 = 8t
\]
\[
64 = 8t
\]
Now, divide both sides by 8:
\[
t = \frac{64}{8} = 8
\]
So, the input \( t \) that results in an output of 176 is \( t = 8 \).

2. **Finding the output for the ordered pair (4, 144)**:
The ordered pair is expressed as \( (t, w) = (4, w) \). We can calculate the output \( w \) when \( t = 4 \):
\[
w = 112 + 8(4)
\]
Calculate the multiplication:
\[
w = 112 + 32
\]
Now, add the numbers:
\[
w = 144
\]
Thus, for the ordered pair \( (4, 144) \), the output is \( w = 144 \), confirming that this pair is correct.

### Summary:
- The input that results in an output of 176 is \( t = 8 \).
- The output in the ordered pair \( (4, 144) \) is \( w = 144 \).