Option C
The expression 20(22 - x) represents the value of the $20 traveler's checks she has.
<u>Solution:</u>
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.
