Let's address the primary problem step-by-step using thorough mathematical reasoning:
### Problem Statement
1. Olivia initially has [tex]$23.
2. She buys 5 bagels, each costing $[/tex]3.
### Solution
Step 1: Initial Money
- Olivia starts with [tex]$23.
\[ \text{Initial Money} = \$[/tex]23 \]
Step 2: Cost per Bagel
- Each bagel costs [tex]$3.
\[ \text{Cost per Bagel} = \$[/tex]3 \]
Step 3: Total Number of Bagels Purchased
- Olivia buys 5 bagels.
[tex]\[ \text{Number of Bagels} = 5 \][/tex]
Step 4: Total Money Spent on Bagels
- To find the total amount of money Olivia spends on bagels, multiply the number of bagels by the cost per bagel.
[tex]\[ \text{Total Money Spent} = \text{Number of Bagels} \times \text{Cost per Bagel} \][/tex]
[tex]\[ \text{Total Money Spent} = 5 \times 3 = \$15 \][/tex]
Step 5: Money Left After Purchase
- Subtract the total money spent on bagels from the initial amount of money Olivia has.
[tex]\[ \text{Money Left} = \text{Initial Money} - \text{Total Money Spent} \][/tex]
[tex]\[ \text{Money Left} = 23 - 15 = \$8 \][/tex]
### Final Answer
Based on the calculations:
- Total Money Spent on Bagels: [tex]$15
- Money Left After Purchase: $[/tex]8
These results can be confirmed as follows:
1. Olivia spends [tex]$15 in total on the bagels.
2. After the purchase, Olivia has $[/tex]8 remaining.
So, the amounts are [tex]$15 spent on bagels and $[/tex]8 left over.
