Question

The bottom cup in a 73 cm tall stack of nested identical cups is 10 cm tall. If each additional cup adds 1.5 cm to the height of the stack, how many total cups are in the stack?

Answer 1

`\boxed{\sf 43 \ cups}`

Explanation:

The stack is 73 cm tall, one cup is 10 cm.

Let’s subtract the height of the one cup from the height of the stack.

`\sf 73 - 10\\=63`

The cups left each add 1.5 cm.

Let x be the cups left.

`\sf 1.5x=63\\x=(63)/(1.5) \\x=42`

Add the 1 to the cups left, because that first cup was subtracted from the height of the stack.

`\sf 42+1\\=43`

Answer 2

43 cups

Explanation:

Subtract the height of the one cup from the stack

73 - 10

63

The rest of the cup each add 1.5 cm to the stack

take the remaining height and divide by 1.5 for each cup

63 cm/ 1.5 cm per cup

42 cup

There are 42 cups in the remaining part of the stack

Plus the 1 cup that is 10 cm

42+1 = 43 cups total in the stack