Final answer:
There are 279 girls and a total of 429 students at the school dance when 65% of the attendees are female and there are 150 boys present.
Step-by-step explanation:
If at a school dance 150 students are boys and 65% are girls, we can calculate the total number of students by finding 65% of the total and then determining what that total must be for 150 to represent the remaining 35%. Let's denote the total number of students as T.
Since 65% are girls, then 35% must be boys because the total must add up to 100%. Therefore, 35% of T is equal to the number of boys:
0.35T = 150
To find T, divide both sides of the equation by 0.35:
T = 150 / 0.35
T = 428.57
Since the number of students must be a whole number, we round up to 429, indicating there is 1 extra boy when rounding the number of boys to the nearest whole number. Therefore, the total number of students at the dance is 429.
By using the total number of students, we can calculate the number of girls by taking 65% of 429:
0.65 × 429 ≈ 279
So, there are approximately 279 girls at the school dance.