Matthew would like to join an online book club that costs $84 per year. If he signs up for an automatic renewal, he will get 5% off his membership. If he signs op in July, he will get an additional 20% off. In addition, for every 2 people he refers to the club, he can get $5 off his membership. How many people does Matthew refer if he pays less than $48 for his membership? Explain.

can't say, without knowing whether or not he got any discounts.

Lets just say He signs up In july, for the 20% discount.

In that case, he gets a $16.80 discount, making his base membership cost $67.20

SO, he gets an additional discount of $19.20 to bring his cost down to $48.

At $5/referral, that would mean 4 referrals would do the trick.

In symbols, we have

84(.8)-5n < 48
67.20 - 5n < 48
-5n < 19.20
n > 3.84

Matthew would like to join an online book club that costs $84 per year. If he signs up for an automatic renewal, he will get 5% off his membership. If he signs up in July, he can get an additional 20% off. In addition, for every 2 people he refers to the club, he can get $5 off his membership. How many people does Matthew refer if he pays less than $48 for his membership?

Well, Matthew's journey to the book club discount land is quite the adventure! Let's break down the math and see how many people he needs to refer to pay less than $48 for his membership.

First, let's calculate the automatic renewal discount. 5% of $84 is $4.20 (let's round it to $4.19 because we all love some quirky numbers). After this discount, Matthew's membership fee will be $79.81.

Next, Matthew lucky Matthew, he gets an additional discount of 20% for signing up in July. This time, 20% of $79.81 is about $15.96 (or $15.96 if we want to stay quirky again). After this discount, Matthew's membership fee will be $63.85.

Now, let's see how many people he needs to refer to bring this amount down to less than $48. For each referral, he receives $5 off the membership fee. Let's call the number of referrals Matthew needs "x".

So, the equation to solve would be: $63.85 - $5x < $48.

If we do a little math-y magic, we get x > 3.37. Since we can't have a fraction of a person, Matthew needs to refer at least 4 people (because 3.37 rounded up is 4) if he wants to pay less than $48 for his membership.

So, Matthew better channel his inner social butterfly and start referring those book-lovers to the club to score that sweet discount!

To determine the number of people Matthew needs to refer in order to pay less than $48 for his membership, we need to consider the discounts he is eligible for.

Let's break down the discounts:

1. Automatic Renewal Discount: Matthew will get a 5% discount if he signs up for automatic renewal. This means he will pay 95% of the original cost, which is $84. So, his cost with the automatic renewal discount is 0.95 * $84 = $79.8.

2. July Sign-Up Discount: If Matthew signs up in July, he will receive an additional 20% off. To calculate the discount, we first need to determine the discounted price after the automatic renewal discount. As calculated earlier, the cost after the automatic renewal discount is $79.8. The 20% discount will be calculated as 20% of $79.8, which is 0.20 * $79.8 = $15.96. Therefore, Matthew's cost after the July sign-up discount is $79.8 - $15.96 = $63.84.

3. Referral Discount: For every 2 people Matthew refers to the club, he can get $5 off his membership. Let's assume Matthew refers x number of people. Then, the discount he will receive based on the number of referrals can be calculated as follows: The number of referrals divided by 2, multiplied by $5. So, the discount based on referrals will be (x/2) * $5.

Now, we can calculate the final cost of Matthew's membership after all the discounts:

Final Cost = Cost after Automatic Renewal Discount - July Sign-Up Discount - Referral Discount

Since we want the final cost to be less than $48, we can write the equation:

Cost after Automatic Renewal Discount - July Sign-Up Discount - Referral Discount < $48

Substituting the values we calculated earlier:

$63.84 - (x/2) * $5 < $48

Simplifying the equation:

$63.84 - $2.5x < $48

Rearranging the terms:

$2.5x > $63.84 - $48

$2.5x > $15.84

Dividing both sides by $2.5:

x > $15.84 / $2.5

x > 6.336

Since the number of referrals cannot be a decimal or fraction, Matthew would need to refer at least 7 people to pay less than $48 for his membership.