One-fourth of the distance between two cities is 100 miles less than two-thirds the distance between the cities. Which equation expresses this situation?
You have two quantities:
One-fourth of the distance
100 miles less than two-thirds the distance
write them was expressions, and equate them.
To express this situation algebraically, let's represent the distance between the cities as 'd'. We can set up the equation as follows:
1/4 * d = 2/3 * d - 100
Explanation:
- We are given that one-fourth of the distance between the two cities is 100 miles less than two-thirds of the distance.
- To express one-fourth of the distance, we multiply it by 1/4. Thus, 1/4 * d represents one-fourth of the distance.
- Similarly, to express two-thirds of the distance, we multiply it by 2/3. Thus, 2/3 * d represents two-thirds of the distance.
- According to the problem, one-fourth of the distance is 100 miles less than two-thirds of the distance. So, we subtract 100 from two-thirds of the distance.
- By equating these two expressions, we get the equation: 1/4 * d = 2/3 * d - 100.