Need help with SAT Math question?

Question

From "The Official SAT" book:

A regulation for riding a certain amusement park ride requires that a child be between 30 inches and 50 inches tall. Which of the following inequalities can be used to determine whether or not a child's height h satisfies the regulation for this ride?

A) |h-10| < 50

B) |h-20| < 40

C) |h-30| < 20

D) |h-40| < 10

E) |h-45| < 5

The book says the answer is D. I don't know how to solve this problem. Can anyone show the steps to solve this?

Thanks!

Answer 1

it should be between 30 and 40

from the solutions it is given in mod so equdiatant from a point so x+y to x-y

solving we get x = 40 an y= 10

so |h-40| &lt; 10 or D

Answer 2

|h - 40| &lt; 10 means h - 40 &lt; 10 (or h &lt; 50) AND -(h - 40) &lt; 10 ( or 40 - 10 &lt; h).  Taking both together, we have 30 &lt; h &lt; 50, which is clearly what thweregulation says.

Answer 3

1.    child&#039;s height  = h

       30 inches &lt; h &lt; 50 inches

2.    30 + 50 = 80

       80 ÷ 2 = 40

  

      40 inches is the middle between  30 inches and 50 inches

3.  you subtract 40inches  from  30 inches , h and 50 inches

    30 inches - 40 inches &lt; h - 40 inches &lt; 50 - 40 inches



     - 10 inches &lt; h - 40 inches &lt; 10 inches

   and it  can be also written as     |h-40| &lt; 10

     which is D

Answer 4

height of child = h

30 &lt; h &lt; 50

You want to change this inequality so you get

-# &lt; h - ?? &lt; +#

where # is the same number.

30 - 40 &lt; h - 40 &lt; 50 - 40

-10 &lt; h - 40 &lt; 10

that can be rewritten as

| h - 40 | &lt; 10

Answer 5

Firstly, the simplest inequality that models this situation is 30&lt;x&lt;50 since the child must be between 30 and 50 inches tall. Then, you would simplify all of them to see which boils down to this inequality. An example:

A) |h-10| &lt; 50

|h-10| &lt; 50 is equal to the inequalities h-10 &lt; 50 and h - 10 &gt; -50

Solve them and combine them to get -40 &lt;h &lt;60. This is not what we are looking for.

Apply this same principle for all of them and you will find that (D) is really 30 &lt; h &lt; 50.

Answer 6

Yes, D is the right answer.

Make the solution symmetric by choosing the value between 30 and 50 or 40, so if the kid is 10&quot; taller he hits the upper limit, if 10&quot; shorter the lower limit.

So the original statement 30&lt;H&lt;50, would become

30-40&lt;h-40&lt;50-40,

just a rewrite by subtracting 40 from each term.

Now  -10&lt;h-40&lt;10  is equivalent to

or |h-40|&lt;10, i.e., answer D.

The statement begs one question, what if the child is exactly either 30 &quot; or 50&quot; tall. Should he be allowed into the ride. According to answer D , if he is 50 &quot; tall, he would not, if he is 30&quot; tall, he also would not, but I think he should. So, a better answer would be

|h-40|&lt;=10.

I hope you like my explanation.

Answer 7

the book is telling you that h (hieght) has to be greater than 30&quot; but less than 50&quot;... so answer D states that h=less than 40&quot; but greater than 10&quot; meaning that the answer D could represent anywhere between 11&quot; and 39&quot;... including the requiements  for the amusement hight (30&quot; to 39&quot;) making  answer D correct in a true statement

Answer 8

if a child must be between the two, the middle value between them is 40, with each extreme (30 or 50) being 10 inches away from this middle (average) value.  So in the equation, if the child is less than ten inches away from 40 inches, it can ride the ride.

if 31 is plugged in the value is 9 so it works, and if 49 is plugged in the value is also 9, so it works again

Answer 9

Since the range of okay values are from 30 inches to 50 inches tall, you should put these values for h in each of the answer selection. Then the left side of the equation should &quot;equal&quot; the right side.

D is the only answer where 30 and 50 are on the border of the inequality. Thus, this is the only thing you need to do to limit the possible answers to 1.