How much does each actually have?

Question

Rose has more money than Connor. If rose gave connor $20, they would have the same amount. While if Connor gave rose $22, rose would have twice as much as Connor. How much does each actually have?

Answer 1

Here's what we know

R - 20 = C + 20 (If Rose has 20 less, that would equal to Conner having 20 more)

R + 22 = 2(C - 22) (Rose having 22 more would be equal to twice Conner, if he has 22 less)

 

Let's solve this with substitution. We'll take the first equation and add 20 to both sides:

R = C + 40

 

We now have a value to a variable, see we can plug it in to the 2nd equation:

C + 40 + 22 = 2(C - 22)

Simplify and distribute:

C + 62 = 2C - 44

Subtract C:

62 = C - 44

Add 44:

106

 

Solving for R now looks like:

R = 106 + 40

And you can check your work from here by plugging the variable values into the 2nd equation.

Answer 2

R - 20 = C + 20        R + 22 = 2(C -22) State the information as numbers and variables

 

       R = C + 40                R = 2C - 66 Simplify both statements

 

       R =  C + 40                                 Solve as simultaneous linear equations (I used subtraction here

       R =2C - 66                                  but substitution would work just as well)  

       0 = -C + 106

 

       C = 106, R = C + 40 = 146