13. The expression 6a + 4c represents the total price, in dollars, of admission to an air show for a adults and c children. On Saturday, 380 adults and 120 children paid admission to the air show. What was the total price of admission for those people?
Answer: C
The total price of admission for 380 adults and 120 children is 2760 dollars.
To calculate the total price of admission, we substitute the values of adults (a = 380) and children (c = 120) into the expression 6a + 4c. This results in 6(380) + 4(120) = 2280 + 480 = 2760 dollars.
A) 524
This option is incorrect because it significantly underestimates the total price. The calculation of the total price using the given expression 6a + 4c results in a much higher value than 524.
B) 2240
This option is also incorrect. While it is closer than option A, it does not reflect the actual calculation based on the expression provided, which results in a total of 2760 dollars.
C) 2760
This is the correct answer. The total price is calculated by evaluating the expression 6(380) + 4(120), which equals 2760 dollars, accurately representing the combined admission cost for 380 adults and 120 children.
D) 5000
This option is incorrect as it overestimates the total price of admission. The calculated total of 2760 dollars does not support such a high figure, making this option invalid.
E) 12000
This option is incorrect as well, as it greatly exceeds the calculated total price of admission. The expression evaluates to 2760 dollars, far lower than 12000.
Conclusion
The correct answer, 2760 dollars, is derived directly from substituting the number of adults and children into the given expression. All other options fail to match the calculated result, either underestimating or overestimating the total price of admission. Thus, option C is definitively the right choice based on the provided data.