To help Theresa determine the cheapest aspect to eliminate in order to stay within her budget, let's go through the process step-by-step:
1. Calculate the Total Cost:
We sum up the costs of all the party aspects:
[tex]\[
\text{Total Cost} = 76.92 \, (\text{Decorations}) + 150.66 \, (\text{Catering}) + 242.15 \, (\text{Musicians}) + 123.36 \, (\text{Refreshments}) + 260.47 \, (\text{Venue})
\][/tex]
Adding these amounts together, the total cost is [tex]\(853.56\)[/tex].
2. Identify the Cheapest Aspect:
Look at the individual costs and determine the least expensive one:
[tex]\[
\text{Cheapest Aspect} = \text{Decorations (76.92)}
\][/tex]
3. Calculate Total Cost After Eliminating the Cheapest Aspect:
Subtract the cost of decorations from the total cost:
[tex]\[
\text{Total Cost After Eliminating Cheapest} = 853.56 - 76.92 = 776.64
\][/tex]
4. Compare with Budget:
Check if the new total cost is within Theresa's budget:
[tex]\[
776.64 \, (\text{Total Cost After Elimination}) > 708 \, (\text{Budget})
\][/tex]
Since 776.64 is still greater than 708, eliminating only the cheapest aspect (decorations) does not keep Theresa within her budget. Nonetheless, identifying Decorations as the cheapest aspect would be the first step in re-evaluating her expenditures in order to stay within budget.
In conclusion, the cheapest aspect of the party that Theresa can eliminate is:
\[
\boxed{\text{Decorations}} \
