Question

PLEASE HELP MATH QUESTION !!! Explain!

Answer 1

When we say two quantities $x$ and $y$ are proportional to one another, there are two ways we could mean this.

- If $x$ is *directly* proportional to $y$, then we mean that as $x$ changes, $y$ changes in the same direction. In other words, if $x$ is in/decreased, then $y$ also in/decreases. The rate of in/decrease doesn't have to be one-to-one; for example, we could have $x$ increase by 1 unit while $y$ would proportionally increase by 5 units. In this case, we'd have $y=5x$.

- On the other hand, if $x$ is *inversely* proportional to $y$, then a change in $x$ results in a change in $y$ that goes in the opposite direction. A common example involves taking a rectangle of constant area and adjusting the width $x$ and length $y$. If the rectangle has an area of 5 square units, then we could have $x=5$ and $y=1$, or we could have $x=4$ and $y=\dfrac54$, or $x=3$ and $y=\dfrac53$, or any combination of $x$ and $y$ such that $xy=5$ is satisfied.

In both cases, we call 5 the "constant of proportionality".

On to your exercises:

(1a) Looks like $a$ stands for number of apples. Then we're told that the cost $c=2.3a$, which means that for every apple, the cost increases by 2.3 dollars. So the constant of proportionality is 2.3. In the language of proportionality, we could then say that the cost of apples is directly proportional to the number of apples by a factor of 2.3.

(1b) 5.4

(1c) 12.5