10 . The local YMCA charges a $$ \$ 79 $$ membership fee and $$ \$ 4350 $$ per month. Allison has a coupon that will allow her to join the club for $$ \$ 298 $$ for 6 months. How much will Allison save if she uses the coupon?

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To determine how much Allison will save by using the coupon, we need to calculate the total cost of the membership with and without the coupon.

### Step 1: Calculate the total cost without the coupon
The YMCA charges a membership fee of $$ \$79 $$ and a monthly fee of $$ \$4350 $$.

1. **Membership Fee**: $$ \$79 $$
2. **Monthly Fee for 6 months**: $$ 6 \times 4350 $$

Let's calculate the total cost without the coupon:

$$
\text{Total Cost without Coupon} = \text{Membership Fee} + \text{Monthly Fee for 6 months}
$$

### Step 2: Calculate the total cost with the coupon
Allison can join the club for $$ \$298 $$ for 6 months.

$$
\text{Total Cost with Coupon} = 298
$$

### Step 3: Calculate the savings
Now, we can find the savings by subtracting the total cost with the coupon from the total cost without the coupon:

$$
\text{Savings} = \text{Total Cost without Coupon} - \text{Total Cost with Coupon}
$$

Now, let's perform the calculations.

1. Calculate the monthly fee for 6 months:
   $$
   6 \times 4350
   $$

2. Calculate the total cost without the coupon:
   $$
   79 + (6 \times 4350)
   $$

3. Finally, calculate the savings:
   $$
   \text{Total Cost without Coupon} - 298
   $$

Let's compute these values.
Calculate the value by following steps:
- step0: Calculate:
  $$79+\left(6\times 4350\right)$$
- step1: Multiply the numbers:
  $$79+26100$$
- step2: Add the numbers:
  $$26179$$
Calculate or simplify the expression $$ 6 * 4350 $$.
Calculate the value by following steps:
- step0: Calculate:
  $$6\times 4350$$
- step1: Multiply the numbers:
  $$26100$$
Calculate or simplify the expression $$ 26179 - 298 $$.
Calculate the value by following steps:
- step0: Calculate:
  $$26179-298$$
- step1: Subtract the numbers:
  $$25881$$
### Calculations Summary:

1. **Monthly Fee for 6 months**: 
   $$
   6 \times 4350 = 26100
   $$

2. **Total Cost without the coupon**: 
   $$
   79 + 26100 = 26179
   $$

3. **Total Cost with the coupon**: 
   $$
   298
   $$

4. **Savings**: 
   $$
   26179 - 298 = 25881
   $$

### Conclusion:
Allison will save **\$25,881** if she uses the coupon.
Allison will save \$25,881 by using the coupon.

10 . The local YMCA charges a \( \$ 79 \) membership fee and \( \$ 4350 \) per month. Allison has a coupon that will allow her to join the club for \( \$ 298 \) for 6 months. How much will Allison save if she uses the coupon?

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