Every 5th customer gets $2 off coupon. Every 7th customer gets $5 coupon and every 15th customer get $20 coupon. Some get 2 prizes and a few get all 3 prizes. If 400 customers come in how many people will get prizes? How much money is given out?

To find the number of customers who will get prizes, we need to calculate the number of customers who meet each condition separately and then add them together.

First, let's calculate the number of customers who get a $2 off coupon. Since every 5th customer gets a $2 off coupon, we can divide the total number of customers (400) by 5.
400 / 5 = 80 customers will get a $2 off coupon.

Next, let's calculate the number of customers who get a $5 coupon. Since every 7th customer gets a $5 coupon, we can divide the total number of customers (400) by 7.
400 / 7 ≈ 57.14 customers will get a $5 coupon.

Lastly, let's calculate the number of customers who get a $20 coupon. Since every 15th customer gets a $20 coupon, we can divide the total number of customers (400) by 15.
400 / 15 ≈ 26.67 customers will get a $20 coupon.

However, we need to keep in mind that some customers can get multiple prizes. To find the total number of customers who will get prizes, we need to consider those who qualify for more than one prize.

To calculate this, we can find the Least Common Multiple (LCM) of the numbers 5, 7, and 15, which will give us the number of customers who will get all three prizes. The LCM of 5, 7, and 15 is 105.

To find the number of customers who will get two prizes, we need to subtract the number of customers who will get all three prizes from the sum of customers who qualify for each individual prize.

80 + 57 + 26 = 163 customers qualify for at least one prize.

163 - 105 = 58 customers will get two prizes.

To find the total number of customers who will get prizes, we can add the customers who qualify for each individual prize, plus the customers who qualify for two prizes, plus the customers who qualify for all three prizes:

80 (get $2 off) + 57 (get $5 off) + 26 (get $20 off) + 58 (get two prizes) + 105 (get all three prizes) = 326 customers will get prizes.

Now, let's calculate the total amount of money given out:

For each $2 off coupon, $2 is given out. Since 80 customers get a $2 off coupon, the total amount given out for $2 off coupons is:
80 customers × $2 off = $<<80*2=160>>160.

For each $5 coupon, $5 is given out. Since 57 customers get a $5 coupon, the total amount given out for $5 coupons is:
57 customers × $5 off = $<<57*5=285>>285.

For each $20 coupon, $20 is given out. Since 26 customers get a $20 coupon, the total amount given out for $20 coupons is:
26 customers × $20 off = $<<26*20=520>>520.

Therefore, the total amount of money given out in prizes is:
$160 + $285 + $520 = $<<160+285+520=965>>965.