Which expression is equivalent to 50x(squared) + 5x(squared) AND The population density of Cedar County is 230: SAT Prep Math
| Which expression is equivalent to 50x(squared) + 5x(squared)? A) 250x(squared) B) 10x(squared) C) 45x(squared) D) 55x(squared) | The population density of Cedar County is 230 people per square mile. The county has a population of 85,100 people. What is the area, in square miles, of Cedar County? |
| This is a simple addition question because x(squared) is common in both terms. We know 50+5 = 55 Therefore, 50x(squared) + 5x(squared) = 55x(squared) You can also check this by taking x(squared) common from both terms, which will give us x(squared)(50+5) Therefore, x(squared)(55) which can also be written as 55x(squared) or 55x^2 | The population density is calculated with the following formula: Population Density = Total Population / Total Area Given that total population is 85,100 and the population density is 230, we get the following: 230 = 85,100 / Total Area We must solve for ‘Total Area’. (Tip, multiply both sides by Total Area and then both sides by 230. Cross out the same terms in the numerator and denominator and we get the following). Total Area = 85,100 / 230 Solving this gives us 370 square miles. |
| The correct answer is D | The area of the country is 370 square miles. |
