Carcass 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 involved 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/
xRewrite with exponents:
10⁸/
96 =
(3)(10⁹) /
xCross multiply to get: (10⁸)(x) = (3)(10⁹)(96)
96 is close enough to 100, so let's replace 96 with 100 to get:
(10⁸)(x) = (3)(10⁹)(100)
or (10⁸)(x) = (3)(10⁹)(10²)
(10⁸)(x) = (3)(10¹¹)
Divide both sides by 10⁸ 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