Can you explain to me the answers in a and b?

Mathematics

1 answer:

Hoochie [10]4 years ago

5 0

a. The constant of proportionality is k = 2

b. If Micah saves $150, his parents will give him $300

<h2>Explanation:</h2>

From mathematics, we know that $y$ varies directly as $x$ or $y$ is directly proportional to $x$ if and only if:

$y=kx$ for some nonzero constant $k$ .

Here we know some facts:

For every $5 that Micah saves, his parents give him $10.

In other words:

Let y be the money his parents give him.

Let x be the money that Micah saves.

$We \ know \ that: \\ y=kx \\ \\ \\ Solving \ for \ k: \\ \\ k=\frac{y}{x} \\ \\ k=\frac{10}{5} \\ \\ \boxed{k=2}$

So,<em> the constant of proportionality is k = 2</em>

In this case, we know that Micah saves $150. So we need to find the amount of his parents will give him. So what we know here is the value of x, because x represents the amount of money Micah saves. Therefore, by knowing x and k, we can calculate the value of y, which is the amount of money his parents will give him. Hence:

$For \ x=150 \ and \ k=2: \\ \\ y=2(150) \\ \\ \boxed{y=300}$