MIllion VS Billion

oquiella wrote:Last year, for every 100 million vehicles that traveled on a certain highway, 96 vehicles were involved in accidents. If 3 billion vehicles traveled on the highway last year, how many of those vehicles were invovled in accidents? ( 1 billion= 1,000,000,000)

A. 288
B. 320
C. 2,880
D. 3,200
E. 28,800

We can use equivalent ratios to solve this.
# cars/# accidents: 100,000,000/96 = 3,000,000,000/x
Rewrite with exponents: 10�/96 = (3)(10�) /x
Cross multiply to get: (10�)(x) = (3)(10�)(96)

96 is close enough to 100, so let's replace 96 with 100 to get:
(10�)(x) = (3)(10�)(100)
or (10�)(x) = (3)(10�)(10²)
(10�)(x) = (3)(10¹¹)
Divide both sides by 10� to get: x = (3)(10³) = 3000

We see that both C and D are close to 3000
However, in our calculations, we replaced 96 with 100, so our calculations are a bit HIGHER than they should be. So, the correct answer must be a little smaller than 3000

Answer: C

Cheers,
Brent