Two quantities compared

The sum of two numbers is two thousand, three hundred and fifty six. Their difference is four hundred and eighteen. Find the greater number. Try it first. Pause if you like. Which part belongs only to the greater number? Think about what remains if we set that part aside. The smaller number is one unit. The greater number is the same unit and four hundred and eighteen more. Set the difference aside. The total now separates into two equal units and the known difference. 2 units equal two thousand, three hundred and fifty six minus four hundred and eighteen, which is one thousand, nine hundred and thirty eight. 1 unit equals one thousand, nine hundred and thirty eight divided by 2, which is nine hundred and sixty nine. One unit is the smaller number. The question asks for the greater number, so include the difference again. The greater number equals nine hundred and sixty nine plus four hundred and eighteen, which is one thousand, three hundred and eighty seven. Subtract the difference before dividing. Then read the question again and build the quantity it asks for.

A bicycle costs two hundred and fifteen dollars more than a scooter. Zhi Hao paid one thousand, one hundred and fifteen dollars for 2 bicycles and 3 scooters. Find the cost of a bicycle. Try it first. Pause if you like. One scooter is one unit. One bicycle is one unit and two hundred and fifteen dollars more. Two bicycles are two units and two extra amounts of two hundred and fifteen dollars. Three scooters are three units. There are 2 bicycles. How many extra amounts must we set aside before finding the equal units? Each bicycle is one scooter unit and two hundred and fifteen dollars more. The 3 scooters are 3 more units. Set aside both extra amounts, one for each bicycle. The 5 equal units remain. 5 units equal one thousand, one hundred and fifteen minus two hundred and fifteen minus two hundred and fifteen, which is six hundred and eighty five dollars. 1 unit equals six hundred and eighty five divided by 5, which is one hundred and thirty seven dollars. One unit gives the scooter cost. Include one extra amount to find the cost of one bicycle. The cost of a bicycle equals one hundred and thirty seven plus two hundred and fifteen, which is three hundred and fifty two dollars. Set aside an extra amount for each bicycle. Find one unit, then add one extra amount for the bicycle asked for.