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

Answer:

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

Step-by-step 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:

$\frac{y_{2}}{y_{1}} = \frac{x_{2}}{x_{1}}$

$y_{2} = \left(\frac{x_{2}}{x_{1}} \right)\cdot y_{1}$ (Eq. 2)

If we know that $x_{1} = 10$, $x_{2}=15$, $y_{1} = 15$, then the amount of pounds of mashed potatoes is:

$y_{2} = \left(\frac{15}{10} \right)\cdot (15)$

$y_{2} = 22.5$

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