Abdul's seventh grade class is going on a field trip to a history museum. There are x students and y teachers going on the trip. Tickets for students are $10 each and tickets for teachers are $20 each. The history museum gave the class 20% off as part of a group promotion.
Pick all the expressions that represent the total cost of the field trip.
a. 1.20(10x)+1.20(20y)
b. 8x+16y
c. 24(x+y)
d. 0.80(10x+20y)
The expressions that represent the total cost of the field trip with a 20% discount must account for the full price of the tickets minus the discount. The full price for student tickets is 10x dollars, and for teacher tickets, it is 20y dollars. A 20% discount means that only 80% of the total cost is paid. Therefore, you must multiply the full price by 0.80 to apply the discount.
Let's evaluate each option:
a. 1.20(10x) + 1.20(20y)
This expression increases the price by 20% rather than applying a discount, so it's not correct.
b. 8x + 16y
This expression seems to have applied the 20% discount after breaking down the full price: 10x becomes 8x (80% of 10x) and 20y becomes 16y (80% of 20y). This is correct.
c. 24(x + y)
This expression does not accurately represent the cost for students and teachers separately and does not apply a 20% discount to the correct original amounts, so it's not correct.
d. 0.80(10x + 20y)
This expression correctly applies a 20% discount to the total cost of student and teacher tickets combined. This is correct.
So the expressions that accurately represent the total cost of the field trip with a 20% discount are:
b. 8x + 16y
d. 0.80(10x + 20y)
pick one
Apologies for any confusion. If we have to choose one expression that correctly represents the total cost of the field trip with the 20% discount, the most accurate one is:
d. 0.80(10x + 20y)
This expression combines the cost for students and teachers before applying the 20% discount, which reflects the group promotion accurately.
To find the total cost of the field trip, we need to multiply the number of students (x) by the cost of their ticket ($10) and the number of teachers (y) by the cost of their ticket ($20). Since there is a 20% discount, we also need to multiply by 0.80 (which represents 100% - 20%) to calculate the reduced cost.
Therefore, the correct expression is:
d. 0.80(10x + 20y)