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 fivedigit number does SERVE represent? V C R + V C C T S E R V E Solutions 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. $20.00  $ 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. $20.00  $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.
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