# Problems solved with linear equations

by Math Student

Problems solved with linear equations, or as commonly known, Algebra word problems.

A bus was driving with 48 passengers, when it reached a stop, x passengers got off and 3 got on. In the next stop, half the passengers got off and 7 got on. There are now 22 passengers, Solve x.

A bus was driving with 52 passengers. When it reached a stop, y passengers got off and 4 got on. In the next stop 1/3 (one-third) of the passengers got off and 3 got on. There are now 25 passengers. Solve y.

- Thank you

Karin from Algebra-Class says:

Problems Solved with Linear Equations
by: Karin

I'll help with the first problem, and then hopefully you'll be able to solve the second problem!

A bus was driving with 48 passengers, when it reached astop, x passengers got off and 3 got on. In the next stop, half the passengers got off and 7 got on. There are now 22 passengers, Solve x.

48 - x + 3 (x got off - subtract - and three got on - add)

48 - x + 3 this simplifies to:
51 - x (48+3 = 51)

So, now we have 51-x.

51-x - .5(51-x) + 7 = 22 (1/2 of the passengers means to multiply 1/2 times the # of passengers which at this point all we know is that there are 51-x passengers) Plus add 7 since 7 got on. This all equals 22 passengers.
Here's our final equation:

51-x - .5(51-x) + 7 = 22

51-x - 25.5 + .5x + 7 = 22

Now combine like terms.

51 - 25.5 + 7 - x+.5x = 22
32.5 -.5x = 22

Now subtract 32.5 from both sides.

32.2 - 32.5 - .5x = 22 - 32.5
-.5x = -10.5

Now divide by -.5 on both sides

-.5x/-.5 = -10.5/-.5

x = 21

X = 21 passengers.

Check by following the story:

48 - 21 +3 - 1/2(30)+7 = 22
22=22

It works!!!

Best of luck!

Karin

### Comments for Problems solved with linear equations

Average Rating     Mar 09, 2013 Rating     FIND 3 CONSECUTIVE by: MERICK hi!i have a problem this is my problem, please help me:FIND THREE CONSECUTIVE NUMBERS SUCH THAT THE SUM OF THE FIRST AND THE THIRD IS 23 MORE TAN THE SECOND, I HOPE FOR YOUR KINDLY CONSIDERATION TO ANSWER THIS PROBLEM. THANK U!Karin from Algebra Class says:If you have 3 consecutive integers, we can identify those integers as: x, x+1, and x+2.The problem states that the sum of the first and third is 23 more than the second. This means:first (x) + third (x+2) = second (x+1) + 23 (23 more).Or: x + x+2 = x+1 +23Now, solve for x.x+x+2 = x+1 + 232x+2 = x+24 (Combine like terms)2x-x +2 = x-x +24 (Subtract x from both sides)x+2 = 24x+2-2 = 24 -2 (Subtract 2 from both sides)x = 22If x = 22, then the other two numbers are 23 and 24 since the numbers are consecutive.Check:22 + 24 = 46 Is this 23 more than the second number (23)? 46 - 23 = 23. yes!!So, the three numbers are: 22, 23, and 24.Hope this helps!Karin

 Jun 29, 2011 Rating     thanks by: Anonymous Thank you. This was very nice to help Need More Help With Your Algebra Studies?