1) A square is divided into three congruent rectangles as shown below. Each of the three rectangles has a perimeter of 16 meters. How many meters are in the perimeter of the square?
2) A person made a purchase for D dollars and C cents, and gave the cashier a $20 bill. The cashier incorrectly charged the person C dollars and D cents, and returned $4.88 in change. If the cashier had charged the correct price, what would the correct change have been?
3) In the addition problem below, different letters stand for different digits. What five-digit number does SERVE represent?
V C R
+ V C C T
S E R V E
1) Let 3S represent the length of a side of the square as shown in the diagram below. Then the perimeter of one of the congruent rectangles is 8S or 16. It follows that S = 2, and 3S, the length of a side of the square, is 6. Therefore the perimeter of the square is 24 meters.
2) To find the incorrect charge, subtract $4.88 from $20.
- $ 4.88 incorrect change
$15.12 incorrect charge
The incorrect charge, $15.12, represents C dollars and D cents. Therefore the correct charge is $12.15. To get the correct change, subtract $12.15 from $20.
- $12.15 correct charge
$ 7.85 correct change
3) Find the values of S, V, and E in that order: S = 1, V = 9, E = 0. Substitute those values in the cryptogram.
V C R 9 C R
+ V C C T + 9 C C T
S E R V E 1 0 R 9 0
Clearly R + T in the units column must equal 10 which will yield a carry of 1 in the tens column. So C + C + 1 must end in 9. C can be 9 or 4. But V = 9. So C must be 4. Substitute 4 for C.
9 4 R
+ 9 4 4 T
1 0 R 9 0
Since there is no carry from the tens column, R in the hundreds column must be 3 (and T in the units column must be 7) SERVE is the number 10390.