the plans for your 13th birthday party are well under way. your parents agree to your guest list of 400 people. you decided it would be fun to give out "door' prizes as the guests enter your party. every 5th guest will receive a black ipod touch and every 7th guest will receive a white psp go. if all 400 people attend this grand event, will any leave with both prizes. if so, how many

11 people will get both the prizes.

Step-by-step explanation:

In this question we need to find common integral multiples of 5 and 7 under 400. As you can see in the figure 35th person is the first one to get both ipod and psp. The LCM (least common multiple) of 5 and 7 which is 35 (! I hope you know how to LCM of two integers).

Therefore the integral multiples of 35 will be same as the common multiples of 5 and 7. So, figuring out the number of integral multiples of 35 under 400 will give the answer.

To do that divide the number 400 with 35. On performing the division the quotient will be 11 and the remainder will be 15.

Therefore 11 persons out of 400 will get both the prizes.

Similarly if you want to find the number of person getting ipod then divide 400 with 5. The quotient will be 80. ∴ 80 people will get ipod.

And for psp, divide 400 with 7. The quotient will be 57. ∴ 57 people will get psp.

In these divisions, consider just the quotient, here remainder is of no use.