word problems

Question

The number of crashes fell 43.6% to 2591 crashes after cameras were installed. How many crashes occurred before cameras were installed? translate to an equation, solve, and check. Please, and thank you.

Answer 1

Angela,

 

To solve this problem, we need to determine what the information provided means.  2591 does not represent 43.6% of the answer you are looking for.  Instead it represents the 56.4% of the number of crashes before the cameras installed.  With this information, we set up our direct proportion equation:

 

56.4/100 = 2591/x (x=number of crashes before cameras)

 

2591*100= 56.4*x

259100=56.4x

Divide by 56.4

4593.97=x

Round up to 4594 crashes before cameras installed

 

 

Answer 2

x - 0.436x = 2591

 

Solve for x

 

⇒ x(1 - 0.436) = 2591 ← factor out an x

⇒ x0.564 = 2591

⇒ x = 2591 / 0.564

= 4593.97

 

Shortcut: original amount = (end amount) / (% remaining)

Answer 3

Hi Angela, So the first thing that you should do is understand the question and what they're asking for. Also what does 43.6%, and 2591 represent in the problem. So it looks like the number of crashes after the cameras were installed decreased to 2,591 and that decrease was 43.6% of the number of crashes before the cameras were installed. Let x represent the number of crashes before the cameras were installed. What we are trying to find is: 2,591 is 43.6% of what number where that number is x.

 

 

Translates to......  2,591 = 0.436 * x    or   2591=0.436x

 

Recall that the word "is" translates to equals "=" and the word "of" translates to multiplication "*". Also remember to change 43.6% to a decimal 0.436.(divide by 100 or simply move the decimal point twice to the left.)

 

             1)     2591=0.436x                             divide by 0.436 on both sides

 

                x=2591/0.436

 

       x=5942.660550458716

       or roughly x=5943 if you round. It wouldn't make sense if you had decimals because it doesn't sound right to have an 1/8 of a crash for example.

 

You can plug x into equation #1 to check your work. Hope this helps