Abdul's 7th grade class is going on a field trip to a history museum there are ex-students and why teachers going on the trip tickets for students are $10 each and tickets for teachers are $20 each History museum gave the class 20% off as part of a group promotion
Let's assume there are x students and y teachers going on the trip.
The total cost of the tickets for the students is $10 * x.
The total cost of the tickets for the teachers is $20 * y.
If the history museum gives a 20% discount, the total cost of the tickets after the discount will be 80% of the original cost.
So, the discounted cost for the students' tickets is 0.8 * ($10 * x) = $8x.
And the discounted cost for the teachers' tickets is 0.8 * ($20 * y) = $16y.
We know that the class has ex-students and teachers going on the trip. So we can write the equation:
x + y = c [where c represents the total number of people going on the trip]
Since the class has a total of 20% off, the cost of the students' tickets plus the cost of the teachers' tickets is 0.8 * [($10 * x) + ($20 * y)].
So, we can write another equation:
8x + 16y = 0.8 * [($10 * x) + ($20 * y)]
Simplifying the equation, we get:
8x + 16y = 8x + 16y
Since the equation remains the same after simplification, it indicates that the equation is true for all values of x and y.
Therefore, the cost of the tickets after the 20% discount is equal to the total cost of the tickets before the discount for the students and teachers.