Question

It takes 10 pounds of potatoes to make 15 pounds of mashed potatoes. At this rate:

How many pounds of mashed potatoes can they make with 15 pounds of potatoes?

Answer 1

22.5 pounds of mashed potatoes are made from 15 pounds of potatoes.

Explanation:

According to the statement, we notice that the amount of pounds of potatoes (
`x`) is directly proportional to the amount of mashed potatoes (
`y`). That is:

`y\propto x`

`y = k\cdot x` (Eq. 1)

Where
`k` is the proportionality constant, dimensionless.

Then we eliminate such constant by building this relationship:

`(y_(2))/(y_(1)) = (x_(2))/(x_(1))`

`y_(2) = \left((x_(2))/(x_(1)) \right)\cdot y_(1)` (Eq. 2)

If we know that
`x_(1) = 10`,
`x_(2)=15`,
`y_(1) = 15`, then the amount of pounds of mashed potatoes is:

`y_(2) = \left((15)/(10) \right)\cdot (15)`

`y_(2) = 22.5`

22.5 pounds of mashed potatoes are made from 15 pounds of potatoes.