Ari had twice as much money as Rita. After Ari spent $800 and Rita spent $240 both of them had the same amount of money left .how much money did each of them have at first

Let's assume Rita had x dollars initially. According to the given information, Ari had twice as much money as Rita, so Ari had 2x dollars initially.

After Ari spent $800, Ari had (2x - 800) dollars left.
After Rita spent $240, Rita had (x - 240) dollars left.

According to the problem, both of them had the same amount of money left. So we can set up an equation:

2x - 800 = x - 240

To solve the equation, we can subtract x from both sides:

2x - x = -240 + 800

This simplifies to:

x = 560

Now we can substitute the value of x back into the equations to find the initial amounts of money:

Rita had x dollars initially, which is 560 dollars.
Ari had 2x dollars initially, which is 2 * 560 = 1120 dollars.

Therefore, Rita had $560 and Ari had $1120 initially.

To find out how much money Ari and Rita had at first, let's break down the information provided:

1. Initially, Ari had twice as much money as Rita. Let's assume Rita had $x, which means Ari had $2x.

2. After Ari spent $800, Ari's remaining amount of money is $2x - $800.
After Rita spent $240, Rita's remaining amount of money is $x - $240.

3. According to the problem, both of them had the same amount of money left after their expenses, so we can set up an equation:
$2x - $800 = $x - $240

Now let's solve the equation to find the value of x:

$2x - $800 = $x - $240

Rearranging terms:
$2x - $x = $800 - $240

Simplifying:
$x = $560

Now that we know Rita had $560, we can find out how much Ari had by multiplying Rita's amount by 2:

Ari's amount = 2 * $560 = $1120

Therefore, Ari initially had $1120 and Rita initially had $560.

A= 2R

A-800=R-240

2R -800 = R -240
R = 560
A = 1120