Alright! Let's break down the problem and find the polynomial that represents the total cost of making [tex]\( y \)[/tex] donuts and [tex]\( y \)[/tex] coffees.
### Step-by-Step Solution:
1. Define the individual costs:
- The cost of making [tex]\( y \)[/tex] donuts is given by [tex]\( 15 + 5y \)[/tex].
- The cost of making [tex]\( y \)[/tex] coffees is given by [tex]\( 6y + 4 \)[/tex].
2. Combine the costs to find the total cost:
To find the total cost of making [tex]\( y \)[/tex] donuts and [tex]\( y \)[/tex] coffees, we need to add these two expressions together:
[tex]\[
(15 + 5y) + (6y + 4)
\][/tex]
3. Combine like terms:
Let's combine the constants (the numbers without [tex]\( y \)[/tex]) and the coefficients of [tex]\( y \)[/tex] from each expression:
[tex]\[
15 + 4 + 5y + 6y
\][/tex]
4. Simplify the expression:
Now, add the constants and the coefficients of [tex]\( y \)[/tex]:
- Constants: [tex]\( 15 + 4 = 19 \)[/tex]
- Coefficients of [tex]\( y \)[/tex]: [tex]\( 5y + 6y = 11y \)[/tex]
5. Write the expression in standard form:
The standard form of a polynomial is written as the sum of terms arranged in descending powers of the variable (in this case, [tex]\( y \)[/tex]).
So, the simplified polynomial that represents the total cost is:
[tex]\[
19 + 11y
\][/tex]
### Final Answer:
The polynomial in standard form that represents the total cost to make [tex]\( y \)[/tex] donuts and [tex]\( y \)[/tex] coffees is:
[tex]\[
\boxed{19 + 11y}
\][/tex]
