Question

Three aluminum cans can be recycled to make a new can. How many new cans can eventually be made from 243 aluminum cans? (Remember that the first new cans that are made can then be recycled into even newer cans!) Do not include the original 243 cans in your count.

Answer 1

121 new cans can eventually be made from 243 aluminum cans

Explanation:

Unit rate defined as the rates are expressed as a quantity 1 such as 2 miles per second or 5 kilometer per hour.

As per the statement:

Three aluminum cans can be recycled to make a new can.

Unit rate per aluminium can =
`(1)/(3)` new can

We have to find the new cans can eventually be made from 243 aluminum cans.

By definition of unit rate;

`\text{Number of new cans made from 243 cans} = \text{Unit rate per aluminium can} * 243`

Substitute the given values we have;

`\text{Number of new cans made from 243 cans} = (1)/(3) * 243 = 81`

Again do the same process:

Number of new can made from 81 can is
`(1)/(3) \cdot 81 = 27`

Similarly,

Number of new cans made from 27 can =
`(1)/(3) \cdot 27 = 9`

Number of new cans made from 9 can =
`(1)/(3) \cdot 9 = 3`

Number of new cans made from 3 can =
`(1)/(3) \cdot 3 = 1`

Now, No further new can made.

Therefore, total new can made from 243 is 81+27+9+3+ 1 =121 cans