For her vacation Mrs. Andrews bought $300 worth of traveler's checks in $10 and $20 denominations. If she has 22 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?
number of 10's --- x
number of 20's ---- 22-x
10x + 20(22-x) = 300
10x + 440 - 20x = 300
-10x = -140
x = 14
She bought 14 10's and 8 20's
check: 14+8 = 22 check!
10(14) + 20(8) = 300 check!
BTW, time to update that textbook, I wonder how many people under 30 would even know what a traveler's check is.
To solve this problem, let's set up an equation to represent the given information.
Let the number of $10 traveler's checks be represented by x, and the number of $20 traveler's checks be represented by (22 - x) since Mrs. Andrews has a total of 22 traveler's checks.
To find the value of the $20 traveler's checks, we need to multiply the number of $20 traveler's checks by $20:
Value of $20 traveler's checks = ($20) * (number of $20 traveler's checks)
= ($20) * (22 - x)
Thus, the expression that represents the value of the $20 traveler's checks is ($20) * (22 - x).
To determine the number of $10 and $20 traveler's checks Mrs. Andrews has, let's use algebra to solve the problem.
Let x represent the number of $10 traveler's checks she has.
Then, 22 - x represents the number of $20 traveler's checks she has.
We are given that Mrs. Andrews bought $300 worth of traveler's checks. The value of each $10 traveler's check is $10, and the value of each $20 traveler's check is $20.
Therefore, the equation representing the total value of the traveler's checks is:
10x + 20(22 - x) = 300
Simplifying this equation will help us find the value of x, which represents the number of $10 traveler's checks.
Rewriting the equation:
10x + 440 - 20x = 300
Subtracting 440 from both sides:
10x - 20x = 300 - 440
Combining like terms:
-10x = -140
Dividing both sides by -10:
x = 14
So, Mrs. Andrews has 14 $10 traveler's checks.
To find the number of $20 traveler's checks, we subtract the number of $10 traveler's checks from the total number of traveler's checks:
22 - x = 22 - 14 = 8
Therefore, Mrs. Andrews has 8 $20 traveler's checks.