Algebra Word Problem Solutions: March 2009

Tuesday, March 17, 2009

Number Problem 6 Solution

This is the solution to the number problem # 6.

In the following Algebra number word problem we have a 3 digit number which has a 100's digit 3 more than the 1's digit and its 10's digit is twice the 100's digit. When all 3 digits are added together, it is equal to 9. What is the number?

If you make the 1's digit x then you have:

100's digit = x + 3 and the

10's digit = 2(x + 3) or 2x + 6

Now when all these digits are added together you get 9 so...

x + x + 3 + 2x + 6 = 9

4x = 0

x = 0

so if x = 0(the 1's digit) then the 100's digit would be 0 +3 or just 3 and the 10's digit would be 0 + 6 or 6.

so the answer is 360

Friday, March 13, 2009

Time and Distance Problem 8 Solution

This is the solution to the algebra time and distance word problem # 8:

Distances in this problem are equal, and rate multiplied by time is equal to distance. You have what the times are--- 4 and 5 hours and and the rates are ( x + 15 ) for with the wind of 15 miles per an hour and ( x - 15) for against the wind at 15 miles per an hour.

So we have...

4( x + 15 ) = 5( x - 15 )

4x + 60 = 5x - 75

x = 135 --> This is how fast the vehicle is moving. But with the wind its 135 + 15 or 150 miles an hour going and 135 - 15 or 120 miles an hour coming back.

To check this 4(150) = 5(120) 600 = 600 ---> You also now know the distance was 600 miles, which was not asked in the problem.

Time and Distance Problem 7 Solution

Here's is the answer to the algebra word time and distance problem # 7:

If Bill is averaging 60 miles per an hour and Craig doesn't leave until 2 hours at 90 mi/hour, then that means that Bill traveled 60 mi/hr * 2 hr = 120 miles before Craig even left. Now how much faster is 90 miles an hour than 60 ? 90 - 60 = 30(this is the net gain of Bill which is what were worried about since were trying to figure out when he will catch up). So the question then becomes how long would it take you going 30 miles per an hour to go 120 miles --- 120/30 =4 So it takes 4 hours hours for Craig to catch him and since he was going 90 miles an hour he went a total of 90 * 4 or 360 miles.

Algebraically>..

90x = 60x + 120

30x = 120

x = 4

90(4) = 360