When solving a word problem with simultaneous equations, the basic method is to choose two variables and set up two equations.
Steps for Solving
① Let the two unknown quantities be x and y (state the units)
② Set up two equations from the problem
③ Solve the simultaneous equations
④ Check whether the values found satisfy the conditions of the problem
⑤ Write the answer in a sentence
Example ①
The sum of two numbers is 20, and their difference is 6. Find the two numbers.
Solution: Let the larger number be x and the smaller number be y: { x+y=20、x−y=6. Elimination method: 2x=26→x=13,y=7。13 and 7
The sum of two numbers is 20, and their difference is 6. Find the two numbers.
Solution: Let the larger number be x and the smaller number be y: { x+y=20、x−y=6. Elimination method: 2x=26→x=13,y=7。13 and 7
Key Points
- State at the beginning what x and y represent
- Set up two equations from two different conditions
- Be sure to check whether the solution satisfies the conditions of the problem, such as being a natural number or a positive number
Practice Problems
- The sum of two numbers is 15, and their difference is 3. Find the two numbers.
- There are two numbers, a larger and a smaller. The larger number is 3 greater than twice the smaller number, and their sum is 21. Find the two numbers.
Answers and Explanations
- Answer:9 and 6. x+y=15、x−y=3→x=9,y=6。
- Answer:15 and 6. x=2y+3、x+y=21→3y+3=21→y=6,x=15。