If the crime rate in a certain region dropped by 28% last year to a rate of 500 crimes per 100,000 citizens, what was the approximate rate before the drop?
A. 500 crimes per 128,000 citizens
B. 640 crimes per 128,000 citizens
C. 695 crimes per 128,000 citizens
D. 640 crimes per 100,000 citizens
E. 695 crimes per 100,000 citizens
OA E
Source: Veritas Prep
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If the crime rate in a certain region dropped by 28% last
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BTGmoderatorDC
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Since the rate dropped by 28%, the current rate is equal to 72% of the previous rate:BTGmoderatorDC wrote:If the crime rate in a certain region dropped by 28% last year to a rate of 500 crimes per 100,000 citizens, what was the approximate rate before the drop?
A. 500 crimes per 128,000 citizens
B. 640 crimes per 128,000 citizens
C. 695 crimes per 128,000 citizens
D. 640 crimes per 100,000 citizens
E. 695 crimes per 100,000 citizens
500/100,000 = 72/100 * x
x = (500*100)/(72*100,000)
x ≈ (7*100)/100,000
x ≈ 700 per 100,000
The correct answer is E.
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Let x be the number of crimes per 100,000 citizens, before the drop. We can create the equation:BTGmoderatorDC wrote:If the crime rate in a certain region dropped by 28% last year to a rate of 500 crimes per 100,000 citizens, what was the approximate rate before the drop?
A. 500 crimes per 128,000 citizens
B. 640 crimes per 128,000 citizens
C. 695 crimes per 128,000 citizens
D. 640 crimes per 100,000 citizens
E. 695 crimes per 100,000 citizens
OA E
Source: Veritas Prep
0.72x = 500
x ≈ 695
Alternate Solution:
We can use the percent change formula: (New - Old)/Old x 100%. Since the % change was a decrease, we consider it as -28%:
(500 - Old)/Old x 100 = -28
(500 - Old)/Old = -0.28
Letting Old = x, we have:
(500 - x)/x = -0.28
500 - x = -0.28x
500 = 0.72x
694.4 = x
695 = x
Thus, the previous rate was 695 crimes per 100,000.
Answer: E
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