Examining a savings plan for college Reuben wants to attend a college that will cost $$ \$ 24,600 $$ for the first year. His uncle gave him a special gift of $$ \$ 3000 $$ to use toward the cost. Reuben plans to attend the college in 6 years. How much must Reuben save each month to have enough for the first-year cost? $$ \$ \square $$

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UpStudy AI · Accepted Answer

To determine how much Reuben must save each month for his college expenses, we can follow these steps:

1. **Identify the total cost of college for the first year.**
   - The total cost is $$ C = 24600 $$.

2. **Subtract the gift from his uncle.**
   - The amount from his uncle is $$ G = 3000 $$.
   - The remaining amount that Reuben needs to save is:
     $$
     R = C - G = 24600 - 3000
     $$

3. **Calculate the remaining amount.**
   - Let's perform the calculation for $$ R $$:
     $$
     R = 24600 - 3000
     $$

4. **Determine the time frame for saving.**
   - Reuben plans to save for $$ T = 6 $$ years. Since he will save monthly, we convert years to months:
     $$
     T_{months} = T \times 12 = 6 \times 12
     $$

5. **Calculate the monthly savings required.**
   - The monthly savings $$ S $$ can be calculated using the formula:
     $$
     S = \frac{R}{T_{months}}
     $$

Now, let's perform the calculations step by step.

First, we will calculate $$ R $$ and $$ T_{months} $$. Then, we will find $$ S $$.

Let's proceed with the calculations.
Calculate the value by following steps:
- step0: Calculate:
  $$6\times 12$$
- step1: Multiply the numbers:
  $$72$$
Calculate or simplify the expression $$ 24600 - 3000 $$.
Calculate the value by following steps:
- step0: Calculate:
  $$24600-3000$$
- step1: Subtract the numbers:
  $$21600$$
Calculate or simplify the expression $$ 21600 / 72 $$.
Calculate the value by following steps:
- step0: Calculate:
  $$\frac{21600}{72}$$
- step1: Reduce the numbers:
  $$\frac{300}{1}$$
- step2: Calculate:
  $$300$$
Now that we have the necessary calculations:

1. The remaining amount Reuben needs to save is:
   $$
   R = 24600 - 3000 = 21600
   $$

2. The total number of months he will save is:
   $$
   T_{months} = 6 \times 12 = 72
   $$

3. The monthly savings required is:
   $$
   S = \frac{R}{T_{months}} = \frac{21600}{72} = 300
   $$

Thus, Reuben must save **$300** each month to have enough for the first-year cost of college.

The final answer is:
$$
\$ 300
$$
Reuben must save \$300 each month.

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