Question: How much less does each person pay after A joins J, P, and D for a meal, if the total bill is x?
Solution:
- Initially, the total bill is x, which is shared by J, P, and D. There are three people sharing the bill. The amount each person pays is calculated by dividing the total bill by the number of people:
Amount each person pays initially = x/3. - After A joins, the number of people sharing the bill increases to 4. The bill x is now divided by 4:
Amount each person pays after A joins = x/4. - To find out how much less each person pays, we subtract the amount each pays after A joins from the amount each pays initially. This involves subtracting one fraction from another:
Reduction in the amount each person pays = (x/3) – (x/4). - To subtract the fractions, we find a common denominator, which is 12 in this case. We convert each fraction to have this common denominator:
x/3 becomes 4x/12 (because 3 times 4 equals 12) and x/4 becomes 3x/12 (because 4 times 3 equals 12). - Now we subtract the two fractions:
(4x/12) – (3x/12) = (4x – 3x) / 12 = x/12.
Therefore, after A joins, each person pays x/12 less than what they were paying initially.