Question

Isabel is buying 6 angelfish, and she wants her total to be no more than $2 above or below $36. Which inequality models the cost x, in dollars, of an angelfish?

A) |36+6x|<2
B) |6x+2|<36
C) |6x-2|<36
D) |36-6x|<2

(each < has a line under it)

Answer 1

Number of fish to be bought = 6

Price of each fish = x

⇒ Total price of fish bought = 6x

We know that the total cost can not be $2 more or less than $36

⇒ 36-2 ≤ 6x ≤ 36+2

⇒ 34 < 6x ≤ 38

Let's look at all the options and see which equation matches the above inequality.

A) |36+6x| ≤ 2

Since the above is a mod function, it can be written as:

⇒ -2 ≤ 36+2x ≤ 2

⇒ -38 ≤ 2x ≤ -34

⇒ -19 ≤ x ≤ -17

This doesn't match with the above. Hence, this is not the correct option.

B) |6x+2| ≤ 36

⇒ -36 ≤ 6x+2 ≤ 36

⇒ -38 ≤ 6x ≤ 34

This also doesn't match with the required inequality. Hence, this option is not correct

C) |6x-2|<36

⇒ -36 ≤ 6x-2 ≤36

⇒ -34 ≤ 6x ≤ 38

This also doesn't match with the required inequality. Hence, this option is not correct

D) |36-6x| ≤ 2

⇒ -2 ≤ 36-6x ≤ 2

⇒ -38 ≤ -6x ≤ -34

Multiplying the above by -1

⇒ 38 ≥ 6x ≥ 34

or 34 ≤ 6x ≤ 38

This inequality matches with the required one. Hence, D is the correct option.