To determine the total cups of coffee made by both Milo and Jax, we need to find the sum of their individual contributions. We are given two functions that represent the number of cups of coffee made by Milo and Jax today:
1. [tex]\( f(x) = 8x - 10 \)[/tex] (cups of coffee made by Milo)
2. [tex]\( g(x) = 3x + 5 \)[/tex] (cups of coffee made by Jax)
To find the total number of cups of coffee made by both, we need to add these two functions together:
[tex]\[ \text{Total coffee} = f(x) + g(x) \][/tex]
Let's perform the addition:
[tex]\[
\begin{align*}
\text{Total coffee} &= (8x - 10) + (3x + 5) \\
&= 8x + 3x - 10 + 5 \\
&= 11x - 5
\end{align*}
\][/tex]
So, the function that represents the total cups of coffee made by Milo and Jax today is:
[tex]\[ \text{Total coffee} = 11x - 5 \][/tex]
Let's now verify this with a specific value of [tex]\(x\)[/tex], say [tex]\( x = 1 \)[/tex]:
1. For [tex]\( x = 1 \)[/tex]:
[tex]\[
f(1) = 8(1) - 10 = 8 - 10 = -2
\][/tex]
[tex]\[
g(1) = 3(1) + 5 = 3 + 5 = 8
\][/tex]
2. Therefore, the total cups of coffee when [tex]\( x = 1 \)[/tex] is:
[tex]\[
\text{Total coffee} = f(1) + g(1) = -2 + 8 = 6
\][/tex]
Thus, when [tex]\( x = 1 \)[/tex], we have:
- Milo made [tex]\(-2\)[/tex] cups of coffee.
- Jax made [tex]\(8\)[/tex] cups of coffee.
- Together, they made a total of [tex]\(6\)[/tex] cups of coffee.
In conclusion, the function representing the total cups of coffee made by Milo and Jax today is [tex]\( 11x - 5 \)[/tex], and with [tex]\( x = 1 \)[/tex], the total is [tex]\( 6 \)[/tex] cups, with individual counts of [tex]\( -2 \)[/tex] for Milo and [tex]\( 8 \)[/tex] for Jax.
