Can anyone teach me the way of solving this problem? a store runs a promotion in which every 500th customer (500th, 1000th, 1500th, received a free gift, every 800th (800th, 1600th, customer receives a voucher, and every 1200th (1200th, 2400th, customer receives a discount. which lucky customer will be the first to receive all three promotional prizes?

let me put a little differently.

the lucky customer will be one that is divisible by 500, 800 and 1200 simultaneously, namely that is the LCD, Least Common Divisor.

now, we can simplify that a little, let's chop off two zeros from all, and only use 5, 8 and 12, to get the LCD and then we'll put back the two zeros, you can think of getting a common factor of 100, 100(5, 8, 12).

so now let's do some quick prime factoring on them. Let's find the LCD of 5 and 8.

5 = 5 only factor

8 = 2*2*2

5 and 8 have no factors in common, thus their LCD is just 5*2*2*2, 40.

Let's find the LCD of 40 and 12

40 = 5*2*2*2

12 = 2*2*3

the 2 is twice in 12, and twice in 40, therefore, we'll use it in the LCD only once, namely we won't use 2*2*2*2, instead we'll only use 2*2. The 40 has an extra 2 and a 5, we'll use those and the 12 has an extra 3, we'll use that.

so, using the repeated factors in both only once, we end up with an LCD of 2*2*2*5*3 = 120, and if we put back the two zeros, that's 12000.

the 12000th customer is divisible by 500, 800 and 1200 simultaneously, because 12000 ÷ 500 = 24, 12000 ÷ 800 = 15, and 12000 ÷ 1200 = 10.

so she'll get a free gift, a voucher and a discount, and maybe even some confetti.

answer: the dogs need to shift their focus to human scent.

its because the dogs being trained are for search and rescue thus they need to be able to track humans and their specific scent

hi,

6x times 4 is 24x and 5 times 4 is 20, so the answer is 24x+20.

hope this and for a little humor i am groot.