Abby and Annie have the same number of coins.

Abby has sorted her coins into groups of 80.

Annie has sorted her coins into groups of 75.

They each have less than 2000 coins.

How many coins do they altogether?

2400 coins

Step-by-step explanation:

What we should do is calculate the  Least Common Multiple of 80 and 75, since each of us put together a group with this amount of coins, this way we will know the amount of coins when they are equal.

To obtain the L.C.M

you have to factor both numbers and multiply the numbers whose exponent is the highest, it looks like this:

75 = 5 ^ 3

80 = 2 ^ 4 * 5

We multiply those with the highest exponent,

5 ^ 3 = 75

2 ^ 4 = 16

75 * 16 = 1200.

L.C.M. is 1200.

Since they tell us that they have less than 2000 coins, this is the correct answer, because when assembling these groups in this way, they coincide again in 2400, which is over the limit.

So, each one has 1200 coins, in total it would be:

1200 * 2 = 2400

Between them they have a total of 2400 coins

it would rotate about 180 degrees.