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
Converting from millions to billions is my weak point in word problems.
MIllion VS Billion
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100 million = (10^2)x10^6 = 10^8oquiella 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
Converting from millions to billions is my weak point in word problems.
3 billion = 3 x 10^9
(3 x 10^9 / 10^8 ) * 96
3 * 10 *96 = 2880
ans = c
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We can use equivalent ratios to solve this.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
# 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
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To solve, we will set up a proportion. We know that "100 million vehicles is to 96 accidents as 3 billion vehicles is to x accidents." To express everything in terms of "millions," we can use 3,000 million rather than 3 billion. Creating a proportion, we have: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
100/96 = 3,000/x
Cross multiplying gives us:
100x = 3,000 * 96
x = 30 * 96 = 2,880
Answer: C
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