Let's break down the problem step by step:
1. Yvonne used 5 tablespoons of butter for the first recipe.
2. For the second recipe, she used [tex]\( 10\% \)[/tex] less butter than the first recipe.
[tex]\[
\text{Amount of butter for the second recipe} = 5 - 5 \times 0.10
\][/tex]
3. Calculating the amount of butter for the second recipe:
[tex]\[
5 - 5 \times 0.10 = 5 - 0.5 = 4.5 \text{ tablespoons}
\][/tex]
4. The total amount of butter used in both recipes is:
[tex]\[
5 + 4.5 = 9.5 \text{ tablespoons}
\][/tex]
The given expression for the total amount of butter is [tex]\( 5 + 5 - 5(10\%) \)[/tex]. Simplifying it step by step:
[tex]\[
5 + 5 - 5 \times 0.10 \implies 5 + 5 - 0.5 \implies 10 - 0.5 = 9.5
\][/tex]
We can also rewrite the amount of butter for the second recipe as [tex]\( 5 \times (1 - 0.10) \)[/tex]:
[tex]\[
5 \times 0.90 = 4.5 \text{ tablespoons}
\][/tex]
Thus, another way of writing the total amount of butter used in both recipes is:
[tex]\[
5 + 4.5
\][/tex]
Since [tex]\( 4.5 = 5 \times 0.90 \)[/tex], another expression to represent the total amount of butter is:
[tex]\[
5 + 5(0.9)
\][/tex]
Now let's evaluate the given choices to see which one matches:
A. [tex]\( 10 - 5\% \)[/tex]
B. [tex]\( 10 - 50\% \)[/tex]
C. [tex]\( 5 + 5(0.9) \)[/tex]
D. [tex]\( 5 + 5(1 - 10) \)[/tex]
We see that the correct expression is:
[tex]\[
C. \quad 5 + 5(0.9)
\][/tex]
