For her vacation mrs. andrews bought $300 worth of traveler's checks in $10 and $20 denominations
travelers checks in all, how many of each denomination does she have?
let x represent the number of $10 traveler's checks she has

⍟ which expression represents the value of the $20
traveler's checks she has? ⍟

a. 20x
b. 20(22)
c. 20(22 - x)

Option C

The expression 20(22 - x) represents the value of the $20  traveler's checks she has.

Solution:

Given, For her vacation Mrs. Andrews bought $300 worth of traveler's checks in $10 and $20 denominations travelers checks in all,  

We have to find how many of each denomination does she have?

Let x represent the number of $10 traveler's checks she has,

Then, $10(x) + $20(number of $20 checks) = 300

10x + 20($20 checks) = 300

x + 2(number of $20 checks) = 30 ⇒ (1)

Now let us see the given options, for value of $20 checks,

It should be in format, that, $20 x number of $20 checks  

⇒ 20(total checks - $10 checks) ⇒ 20(total checks – x), as we can see only C is in that format, it is correct and total number of checks = 22.

Then, (1) ⇒ x + 2(22 – x) = 30

⇒ x + 44 – 2x = 30

⇒2x – x = 44 – 30

⇒ x = 14

So, $10 checks count = 14, then, $20 checks count = 22 – 14 = 8.

Hence, there are 14 $10 checks and 8 $20 checks, and option c is correct.