if attendance at a certain high school had incresed by 30 percent over lasy year, this years attendance would have been 1430. In reality, attendance fell by 35 percent from last year. what was this years attendance?
im not sure where to begin...
am i on the right track if i do...
x + 30/100 = 1430
x - 35/100
to get last year's attendance ...
1.3x = 1430
x = 1430/1.3 = 1100
reality ...
this year's was only 65% of last years, (it dropped 35%)
so this year's attendance
= .65(1100) = 715
1.3x=1430
x=1430/1.3=1100 so the attendance from last year
since it fell by 35% last year only 65% is left so
0.65(1100)= 715
so this years attendance was 715 students
To find this year's attendance, we can break the problem into two parts. First, let's find the hypothetical attendance if it had increased by 30 percent. Then, we'll adjust that number by the actual decrease of 35 percent to get the final attendance.
Step 1: Finding the hypothetical attendance if it had increased by 30 percent.
Let's assign a variable to represent last year's attendance, so let's say last year's attendance was 'Y'. According to the problem, this year's attendance, if it had increased by 30 percent, would have been 1430. So we can set up the equation as follows:
Y * (1 + 30/100) = 1430
Simplifying this equation leads us to:
Y * 1.30 = 1430
Step 2: Finding this year's actual attendance.
Now that we have the hypothetical attendance if it had increased by 30 percent, we need to account for the actual decrease of 35 percent. Let's assign a variable to represent this year's actual attendance, so let's say this year's attendance is 'X'. We can now set up the equation as follows:
Y * 1.30 * (1 - 35/100) = X
Substituting the value of Y from the first equation into the second equation, we get:
(1430) * (1 - 35/100) = X
Calculating this equation leads us to:
1000 * (1 - 0.35) = X
1000 * 0.65 = X
650 = X
Therefore, this year's actual attendance is 650.