It is the grand opening of a local supermarket. Every 5th customer will receive a coupon for a free turkey and every 7th customer will receive a coupon for a free half gallon of ice cream. If 400 customers come in on opening day, how many people will get both a coupon for a free turkey and a coupon for a free half gallon of ice cream?
5 and 7 are both prime
so every 35th customer will receive both
400 / 35 = ? ... no fractional customers
80 Will get free turkey and 57 will get free half gallon of ice cream.
i got nothin to it please help me!!!!
Common factors of 5 and 7 in 400.
LCM of 5 and 7 is 35
400/35 = 11R3.
So there are 11 customers in the 400 who will get both.
To find out how many customers will receive both a coupon for a free turkey and a coupon for a free half gallon of ice cream, you need to determine the multiples of both 5 and 7 and find their intersection.
Let's break it down step by step:
Step 1: Find the multiples of 5:
To find the multiples of 5, you can start with 5 and then keep adding 5 to it. The first few multiples of 5 are: 5, 10, 15, 20, 25, 30, 35, 40, ...
Step 2: Find the multiples of 7:
Similarly, to find the multiples of 7, start with 7 and keep adding 7. The first few multiples of 7 are: 7, 14, 21, 28, 35, 42, 49, 56, ...
Step 3: Determine the common multiples:
Now, find the common multiples of 5 and 7, which are the numbers that appear in both lists. Looking at the lists above, we can see that 35 is the first number that appears in both lists.
Step 4: Count the common multiples within the given range:
Since 400 customers come in on opening day, we need to find how many times 35 fits into 400. Divide 400 by 35 to find the quotient: 400 ÷ 35 = 11.43 (approximately). We'll take the whole number part, which is 11.
Step 5: Calculate the number of people who will receive both coupons:
Since every 35th customer will receive both a coupon for a free turkey and a coupon for a free half gallon of ice cream, multiply the whole number part of the quotient (11) by 35 to get the total number of customers who will receive both coupons: 11 × 35 = 385.
Therefore, 385 customers will get both a coupon for a free turkey and a coupon for a free half gallon of ice cream on the grand opening day of the supermarket.