1) I have exactly ten coins whose total value is $1. If three of the coins are quarters, what are the remaining coins?
2) A group of 21 people went to the county fair with 9 people on a stagecoach and 3 people in a buggy. On the return trip, 4 people rode in each buggy. How many people returned on the stagecoach?
3) In the addition problem below, each letter stands for a digit and different letters stand for different digits. What digits do the letters H, E, and A each represent?
+ H E
1) We have to find 7 coins whose value is $0.25. If the coins were nickels, their total value would be too large. There must be at least 5 pennies. Then we need two coins whose value is $0.20. The coins are dimes. Therefore the remaining coins are 5 pennies and 2 dimes.
2) Going to the fair, 12 people rode in the buggies. Since 3 people rode in each buggy, there were 4 buggies. On the return trip, 4 people rode in each buggy. Then 16 people rode in the buggies. Since the total number of people was 21, 5 rode in the coach.
3) In the tens column, H is less than 3. Otherwise the sum would be a three-digit number. H = 1 or 2. In the units column, the sum of 4 Es is an even number. Then H in the sum must be 2. It follows that E must be either 3 or 8. If E = 8, the sum will be a three-digit number. Thus E = 3, H = 2, and A = 9.