To determine whether Sue will have enough money to buy 4 concert tickets in 8 weeks, we need to follow several steps:
1. Initial Savings:
Sue starts with an initial savings of [tex]$100.
2. Savings Every 2 Weeks:
Sue plans to save an additional $[/tex]15 every 2 weeks.
3. Total Number of Weeks:
The total period given is 8 weeks.
4. Number of Saving Periods:
Since Sue saves every 2 weeks, we calculate the number of 2-week periods within 8 weeks:
[tex]\[
\text{Saving Periods} = \frac{\text{Total Weeks}}{2} = \frac{8}{2} = 4
\][/tex]
Therefore, there are 4 saving periods.
5. Total Savings After 8 Weeks:
To find out the total amount Sue will save after 8 weeks, we add the savings from these periods to the initial savings:
[tex]\[
\text{Additional Savings} = \text{Savings Per 2 Weeks} \times \text{Saving Periods} = 15 \times 4 = 60
\][/tex]
[tex]\[
\text{Total Savings} = \text{Initial Savings} + \text{Additional Savings} = 100 + 60 = 160
\][/tex]
Hence, by the end of 8 weeks, Sue will have [tex]$160 in total savings.
6. Cost of Concert Tickets:
Each concert ticket costs $[/tex]50. Sue needs to buy 4 tickets, so the total cost is:
[tex]\[
\text{Total Ticket Cost} = 50 \times 4 = 200
\][/tex]
Therefore, the total cost for 4 tickets is [tex]$200.
7. Comparison of Savings and Cost:
Compare Sue's total savings to the total ticket cost:
\[
\text{Total Savings} = 160 \quad \text{and} \quad \text{Total Ticket Cost} = 200
\]
Since $[/tex]160 is less than [tex]$200, Sue does not have enough money saved to buy 4 concert tickets.
Based on this analysis, we conclude that Sue will not have enough money saved to buy 4 concert tickets costing $[/tex]50 each.
