At a school camp, 30% of the students were boys. When 87 students left the camp after the second day, half the original number of boys were left behind, and the number of girls decreased by 20%. How many girls were at the camp in the beginning?
To start, there were b boys and g girls.
b = 3/7 g
(b+g)-87 = b/2 + 4/5 g
so,
b + 7b/3 - 87 = b/2 + (4/5)(7/3)b
b = 90
so, g = 210
check:
after 87 students left, there were 45 boys and 168 girls. 300-87 = 213 = 45+168
Yes this is grade 7 Singapore math @NOYB
Thanks! :)
Is this Singapore Math?
Why did the math book go to the comedy club? Because it wanted to find the square root of laughter! Now, let's solve this riddle together.
Let's say the total number of students at the camp in the beginning is "x."
We know that 30% of the students were boys, so the number of boys at the camp would be 0.3x.
After 87 students left on the second day, half the original number of boys were left behind, which means only 0.15x boys were left.
We're also told that the number of girls decreased by 20%, which means there were 0.8 times the number of girls in the beginning.
Now, let's put all the information together:
0.15x (boys left) + 0.8x (remaining girls) = x (total number of students)
Simplifying this equation, we get:
0.15x + 0.8x = x
Combining like terms, we have:
0.95x = x
To solve for x, we can divide both sides of the equation by 0.95:
x = x / 0.95
And after simplifying, we get:
x = 1.0526x
So, in the beginning, there were approximately 1.0526 times the number of students at the camp.
But since we're looking for the initial number of girls, and we know that there were 0.8 times the original number of girls, we can divide 1.0526x by 0.8:
1.0526x / 0.8 = 1.3158x
So, the approximate number of girls at the camp in the beginning would be 1.3158 times the number of students.
As we don't have the exact value of x, I'm afraid I can't give you a specific number.
To find out how many girls were at the camp in the beginning, we need to work through a series of steps based on the information given.
Step 1: Calculate the number of boys at the camp in the beginning.
Given that 30% of the students were boys, we can start by assuming the total number of students is 100%.
Therefore, if 30% were boys, then the remaining 70% represents the number of girls. This means that the number of boys can be calculated as 30% of the total number of students.
Let's represent the total number of students as 'X':
Number of boys = 30% of X = 0.3X
Step 2: Calculate the number of boys left after 87 students left the camp.
According to the given information, after the second day, half the original number of boys were left behind.
So, the number of boys left can be calculated as half of the initial number of boys.
Number of boys left = 0.5 * (0.3X)
Step 3: Calculate the number of girls left after 87 students left the camp.
The number of girls decreased by 20%. This means that the number of girls left can be calculated as 80% of the initial number of girls.
Let's represent the initial number of girls as 'Y':
Number of girls left = 80% of Y = 0.8Y
Step 4: Calculate the total number of students left after 87 students left the camp.
The total number of students left can be obtained by subtracting 87 from the initial total number of students, which is X.
Total number of students left = X - 87
Step 5: Formulate an equation based on the information mentioned in Step 2, Step 3, and Step 4.
The total number of students left (Step 4) can be expressed as the sum of the number of boys left (Step 2) and the number of girls left (Step 3).
X - 87 = 0.5 * (0.3X) + 0.8Y
Step 6: Solve the equation to find the value of Y (initial number of girls).
Solve the equation obtained in Step 5 to find the value of Y.
Simplifying the equation:
X - 87 = 0.15X + 0.8Y
Rearranging the equation:
0.8Y = X - 87 - 0.15X
0.8Y = 0.85X - 87
Dividing both sides of the equation by 0.8:
Y = (0.85X - 87) / 0.8
Now we have an equation expressing the initial number of girls, Y, in terms of the initial total number of students, X.
Therefore, to determine the number of girls at the camp in the beginning, we need to know the value of X (the initial total number of students).