i still don't get it ...Our class planned a holiday party for disadvantaged kids.Some of us baked cookies for the party.On the day of the party,we found we could divide the cookies into packets of two, three, four, five, or six and have just one cookie left over in each case.If we divided them into packets of seven, there would be no cookies left over. What is the least number of cookies the class could have baked?__________.
Katherine -- you've had help from three tutors. Now it's your turn to study our answers and follow our directions.
To find the least number of cookies the class could have baked, we need to look for a number that satisfies the given conditions.
First, we know that when dividing the cookies into packets of two, three, four, five, or six, there is always one cookie left over. This means that the number of cookies must be one more than a multiple of 2, 3, 4, 5, and 6.
Let's start by finding the least common multiple (LCM) of 2, 3, 4, 5, and 6. The LCM of these numbers is 60. Therefore, the number of cookies must be 60 plus one (61) since it is one more than a multiple of these numbers.
Now, we need to check if dividing 61 cookies into packets of seven leaves no cookies left over. Divide 61 by 7, and we get a quotient of 8 with a remainder of 5. This means there would be 5 cookies left over when dividing into packets of seven.
Since dividing 61 by seven results in a remainder, it doesn't satisfy the given condition. Therefore, 61 cookies is not the least number the class could have baked.
We should look for another number that satisfies the conditions. Let's multiply 61 by the LCM of 2, 3, 4, 5, and 6, which is 60. This gives us 61 x 60 = 3660 cookies.
Now, let's divide 3660 by 7. The quotient is 522 with no remainder. This means that dividing 3660 into packets of seven leaves no cookies left over.
Thus, the least number of cookies the class could have baked is 3660.