Certainly! Let's break down the solution step-by-step:
### Step-by-Step Solution
1. Initial Values:
- Total money initially: [tex]$23
- Cost per bagel: $[/tex]3
- Number of bagels bought: [tex]$5
- Initial number of computers: $[/tex]9
- Number of computers added each day: [tex]$5
- Number of days computers are added: $[/tex]4
2. Money Spent on Bagels:
To calculate the total amount of money spent on bagels, we multiply the cost per bagel by the number of bagels:
[tex]\[
\text{Money Spent} = 5 \text{ bagels} \times 3 \text{ (dollars per bagel)} = 15 \text{ dollars}
\][/tex]
3. Money Left:
To determine the amount of money left after buying the bagels, subtract the money spent from the initial amount:
[tex]\[
\text{Money Left} = 23 \text{ (initial money)} - 15 \text{ (money spent)} = 8 \text{ dollars}
\][/tex]
4. Computers Added:
Over 4 days, the number of computers added each day is 5. So, we calculate the total number of computers added:
[tex]\[
\text{Computers Added} = 5 \text{ (computers per day)} \times 4 \text{ (days)} = 20 \text{ computers}
\][/tex]
5. Total Number of Computers:
To find the total number of computers after 4 days, add the initial number of computers to the number of computers added:
[tex]\[
\text{Total Computers} = 9 \text{ (initial computers)} + 20 \text{ (computers added)} = 29 \text{ computers}
\][/tex]
6. Solving for [tex]\( k \)[/tex]:
Given the expressions:
[tex]\[
\text{a} = 72, \quad \text{b} = -12, \quad \text{c} = 9, \quad \text{d} = 9
\][/tex]
Calculate the left-hand side (LHS) and right-hand side (RHS) of the equation:
[tex]\[
\text{LHS} = a + b = 72 - 12 = 60
\][/tex]
[tex]\[
\text{RHS} = c + d = 9 + 9 = 18
\][/tex]
Solving for [tex]\( k \)[/tex] involves finding the ratio of LHS to RHS:
[tex]\[
k = \frac{\text{LHS}}{\text{RHS}} = \frac{60}{18} = 3.\overline{3} \approx 3.3333333333333335
\][/tex]
### Summary of Results:
1. Money Spent: [tex]$15$[/tex] dollars
2. Money Left: [tex]$8$[/tex] dollars
3. Computers Added: [tex]$20$[/tex] computers
4. Total Computers: [tex]$29$[/tex] computers
5. Value of [tex]\( k \)[/tex]: [tex]$3.\overline{3} \approx 3.3333333333333335$[/tex]
These are the results for each step of the problem.
