Question

The value of $\tiny\frac{(487{,}000)(12{,}027{,}300) + (9{,}621{,}001)(487{,}000)}{(19{,}367)(.05)}$ is closest to

$10{,}000{,}000$

$100{,}000{,}000$

$1{,}000{,}000{,}000$

$10{,}000{,}000{,}000$

$100{,}000{,}000{,}000$

Answer: D

Concepts:estimation distributive property

Difficulty rating: 890

Solution:

Factor the numerator: $487{,}000$ $\cdot\, (12{,}027{,}300 + 9{,}621{,}001).$

Rounding to leading digits, this is about $500{,}000$ $\times (10{,}000{,}000 + 10{,}000{,}000)$ $= 500{,}000 \times 2$ $\times 10^{7}.$ The denominator is about $20{,}000 \times .05 = 1000.$

So the value is roughly $\dfrac{500{,}000 \times 2 \times 10^{7}}{1000}$ $= 10^{10}$ $= 10{,}000{,}000{,}000.$

Thus, the correct answer is D .

1991 AMC 8 Problem 7

Answer: D

Solution:

Problem 7 in Other Years