John says to Brenda, "if you give me eight dollars, we will have an equal amount of money." Brenda responds, "but if you give me eight dollars, I will have twice as much money as you." How much money did Brenda and John each have?
Need to show how you did this.
J+8=B-8
B+8=2(J-8)
I got this far and still am stuck. How much do they each have?
Solve this system of equations by substitution or elimination.
Substitution would probably be easiest. Simply solve for b in the first equation and substitute that into the second equation.
I have tried substituting J and B with several different numbers and I can't come up with answer. I have been working on this so long and don't get it. How much money do they each have/
That’s wrong... if
X =16 and Y=24 then
16+8=24 and 24-8=16 they don’t have the same amount. Also 16-8=8 and 24+8=32 Brenda does not have twice as much. The answer is John has 40 and Brenda has 56.
40+8=48 and 56-8=48. Equal amounts
40-8=32 and 56+8=64. Twice as much
To solve this problem, let's assign variables to represent the amount of money that John and Brenda each had.
Let's say John had x dollars, and Brenda had y dollars.
According to John, if Brenda gave him eight dollars, they would have an equal amount of money. In other words, John's amount plus Brenda's eight dollars would be equal to Brenda's amount:
x + 8 = y ----(Equation 1)
According to Brenda, if John gave her eight dollars, she would have twice as much money as John. In other words, Brenda's amount plus John's eight dollars would be twice the amount that John had:
y + 8 = 2x ----(Equation 2)
We now have a system of two equations: Equation 1 and Equation 2. Now, we can solve this system of equations by using substitution or elimination method.
Let's use the substitution method to solve the system.
From Equation 1, we can rewrite it as:
x = y - 8 ----(Equation 3)
Now, we can substitute Equation 3 into Equation 2:
y + 8 = 2(y - 8)
Simplifying this equation:
y + 8 = 2y - 16
Rearranging the terms:
2y - y = 8 + 16
y = 24
Now that we have the value of y, we can substitute it back into Equation 3 to find x:
x = 24 - 8
x = 16
Therefore, John had 16 dollars, and Brenda had 24 dollars.
This on is pretty easy, you just have to create 2 equations base on the problem.
X = Jonh
Y = Brenda
X+8 =Y
Y+8 =X
X=Y-8
Y+8=2(Y-8)
Y+8=2Y-16
Y-2Y=-16-8
-Y=-24
Y=-24/-1
Y=24
X=Y-8
X=24-8
X=16
I also post the answer to your other problem... hope that help you at least a little.