Question

solving inequalities in real life 6. The amusement park won't allow kids to ride roller-coasters until they are a minimum of 48 inches tall. Michael is now 42 inches tall, and grows about 1/2 inch every month. How many months will it be until Michael can ride a roller- coaster?

Answer 1

In this case, we would like to model this situation as an inequality.

It says that, in order to ride the roller coaster, you should at least be 48 inches tall. So, when someone wants to ride the roller coaster, his/her height should be greater or equal to 48 inches. This situation can be modeled witht the inequality

$y\ge48$

where y is the height of the person at the moment he/she is trying to ride the roller coaster.

Right now, Michale es 42 inches tall. So he is not able to ride the roller coaster yet.

We are told that he grows 1/2 inch every month. Let x be the months that have passed since we was 42 inches. So, the total amount he grew is

$\frac{1}{2}\cdot x$

After he grew this amount, he will be as tall as the sum of this two quantities, namely,

$42+\frac{1}{2}\cdot x$

Since we want that Michael should be able to ride the roller coaster, his height should be above the given limit, so we get the inequality

$42+\frac{1}{2}\cdot x\ge48$

now, we want to solve this inequality for x. To do so, we subtract 42 on both sides, so we get

$\frac{1}{2}x\ge48-42=6$

Now, we multiply by 2 on both sides, so we get

$x\ge6\cdot2=12$

which means that Michael should wait at least a year (12 months) to ride the roller coaster