algebra word problem

Question

The sum of two numbers is 33. Twice the first number minus the second number equals 18. Find both numbers.

Answer 1

Hello, Colton,

 

     Let's do things in some steps:

 

1.  First, write the equation down, and  underline or highlight every key word or number.

 

     Note:  Since you don't know what the two numbers are call them "X" and "Y."   Let "X" be the first number.

 

                         X+ Y        =  33                                    2X       -                  Y                    = 18

The sum of two numbers is 33.  Twice the first number minus the second number equals 18.  Find both

 

numbers.

 

2.  Now, set up the equations:                   X+Y=33

                                                             2X-y=18 

                                                             3X   = 51  

 

                                                               X=51/3            X=17

                  

 

3.  The system of equations can be solved using the addition method.  Just add both equation up.

 

4.  Then solve for "Y" by picking the easier equation on top and substituting into it:

 

X+Y=33,    17+Y=33       Y=______ 

 

5.  Lastly, check your work by substituting the values for "X" and "Y" into both equations.  If you get true statements, then everything is correct.

 

      I hope that I was helpful.

                                 

                                     Thank you,

 

                                     Susan C

 

 

 

 

 

 

 

 

 

 

 

Answer 2

All right, this problem is just about looking for the two numbers both of which are unknown so there will be two variables, one for each unknown. Let's use x for the first number and y for the second number.

 

We know that "the sum of the two numbers is 33". Since "sum" means addition, then the equation would be: x+y=33. In the other part of the problem, it says "twice the first number minus the second number equals 18."  Because the first number is x, "twice the first number" would be 2x and "minus the second number" would mean that y is subtracted from 2x. This would make the equation be: 2x-y=18.

 

Now that we have two equations with two unknowns, we can rearrange one of the equations to isolate a variable so we can use substitution to solve for the other variable. You can choose either equation to isolate a variable, depending on whether you want to solve for x or y first. We'll solve for x first by rearranging the second equation.

 

2x-y=18 so y must be by itself. To do this we must subtract by 2x on both sides so they cancel: 2x-2x-y=18-2x. This leaves -y=18-2x so the y is isolated but it's negative (there is a -1 in front of it). So, we'll remove the negative by doing the opposite operation (like before, but since -y is -1•y, cancelling means division by -1). The equation will look like: -y/ -1 = (18-2x)/ -1 which make it y=-18+2x or y=2x-18.

 

Substituting y with "2x-18" into the first equation will give: x +2x-18=33. Since the x terms have the same "tag" we can combine like terms so now the equation is 3x-18=33. Like before we must isolate the variable (x in this case) so add 18 to both sides: 3x-18+18=33+18. 3x now equals 51 so divide by 3: 3x/3=51/3 which is 17. Yay, x=17!

 

Substitute "17" as x in the first equation so now its 17+y=33 and solve for y. Doing the math we did before, y should be 16.

 

Double check to make sure the math is correct using 17 for x and 16 for y... does 17+16=33? Does 2(17)-16=18? YES!