if abby gives 10 dollars to ben they will have the same amount of money.If ben gives abby 20 dollars she will have 4 times as much money as ben.How much money dol they each have?

Answer 1

Let's assume Abby has A dollars and Ben has B dollars.

According to the problem statement:

If Abby gives $10 to Ben, then Abby will have the same amount of money as Ben. This can be represented by the equation: A - 10 = B + 10 or A - B = 20.

If Ben gives Abby $20, then Abby will have 4 times as much money as Ben. This can be represented by the equation: B - 20 = 4(A + 20) or B - 20 = 4A + 80.

We can solve for one variable in terms of the other from the first equation:

A - B = 20

A = B + 20

Substituting this expression for A into the second equation gives:

B - 20 = 4(B + 20) + 80

B - 20 = 4B + 100

-3B = -120

B = 40

Therefore, Ben has $40. Using the first equation to solve for A, we get:

A - B = 20

A - 40 = 20

A = 60

Therefore, Abby has $60.

Answer 2

Let's use algebra to solve this problem.

Let's start by defining the amount of money that Abby and Ben have before any transactions as A and B, respectively.

According to the problem statement, if Abby gives 10 dollars to Ben, they will have the same amount of money. This means that after the transaction, Abby will have A - 10 dollars and Ben will have B + 10 dollars. Therefore, we can set up the equation:

A - 10 = B + 10 (Equation 1)

The second part of the problem states that if Ben gives Abby 20 dollars, she will have 4 times as much money as Ben. After this transaction, Abby will have A + 20 dollars, and Ben will have B - 20 dollars. So we can set up another equation:

A + 20 = 4(B - 20) (Equation 2)

Now we have two equations with two variables. We can use Equation 1 to solve for A in terms of B:

A - 10 = B + 10

A = B + 20 (Equation 3)

We can substitute Equation 3 into Equation 2 and solve for B:

B + 20 + 80 = 4B

100 = 3B

B = 33.33 (rounded to two decimal places)

Now we can use Equation 3 to solve for A:

A = B + 20

A = 33.33 + 20

A = 53.33 (rounded to two decimal places)

Therefore, Abby has 53.33 dollars and Ben has 33.33 dollars before any transactions. After Abby gives 10 dollars to Ben, they both have 43.33 dollars. After Ben gives Abby 20 dollars, Abby has 73.33 dollars and Ben has 13.33 dollars, which means Abby has 4 times as much money as Ben.

Answer 3

a - 10 = b + 10,

a = b + $20, Abby has $20 more than Ben

a + 20 = 4(b - 20)

b + 20 + 20 = 4(b - 20)

Can you solve for b and anser?