Ruby had 5 times as much money as Sally. Ruby spent $80 and Sally had 3/7 as much as Ruby in the end. How much did Ruby have at first?
Show your work.
Let x = the amount of money Ruby had at first.
5x = the amount of money Ruby had before spending $80.
5x - 80 = the amount of money Ruby had after spending $80.
3/7(5x - 80) = the amount of money Sally had after Ruby spent $80.
3/7(5x - 80) = 3/7(5x) - 3/7(80)
3/7(5x) = 3/7(80) + 3/7(5x - 80)
3/7(5x) = 3/7(80) + Sally's amount of money
3/7(5x) = 3/7(80) + 3/7(5x - 80)
3/7(5x) = 3/7(80) + 3/7(5x) - 3/7(80)
3/7(5x) = 3/7(5x)
5x = 80
x = 16
Ruby had $16 at first.
Well, let's use a little bot math and humor to solve this problem!
Let's assume that the amount of money Ruby had at first is 'x'.
According to the problem, Ruby had 5 times as much money as Sally, so Sally had (1/5)x.
After Ruby spent $80, Ruby had 'x - 80' money left.
Now it's mentioned that Sally had 3/7 as much as Ruby in the end. So, we can set up an equation:
(1/5)x = (3/7)(x - 80)
Clear those fractions:
7x = 15(x - 80)
Now, let's distribute:
7x = 15x - 1200
Subtract 15x from both sides:
-8x = -1200
Divide by -8:
x = 150
So, Ruby had $150 at first!
Now comes the humor part: Maybe Ruby spent all that money on a fancy clown wig! Or maybe Sally convinced her to invest it all in a helium balloon business! Who knows? The possibilities are endless, my friend!
Let's assume that Sally had x dollars at first.
According to the information given, Ruby had 5 times as much money as Sally. This means Ruby had 5x dollars at first.
After spending $80, Ruby had (5x - 80) dollars remaining.
It is also stated that Sally had 3/7 as much money as Ruby in the end. This can be expressed as (3/7)(5x - 80).
Since we know that Sally initially had x dollars, we can set up the following equation: (3/7)(5x - 80) = x
To solve for x, we can multiply both sides of the equation by 7:
3(5x - 80) = 7x
Expanding the equation, we get: 15x - 240 = 7x
Simplifying the equation, we can subtract 7x from both sides:
15x - 7x - 240 = 0
Combining like terms, we get: 8x - 240 = 0
We can then add 240 to both sides of the equation:
8x = 240
Finally, we can divide both sides of the equation by 8 to solve for x:
x = 30
So, Sally had $30 at first.
Since Ruby had 5 times as much money as Sally, Ruby had 5 * $30 = $150 at first.
To find out how much Ruby had at first, we can use algebra. Let's say that Sally had x dollars originally. According to the problem, Ruby had 5 times as much money as Sally, which means Ruby had 5x dollars at first.
Next, Ruby spent $80, which means she had 5x - 80 dollars left. The problem states that Sally had 3/7 as much money as Ruby in the end, so we have the equation:
3/7 * (5x - 80) = x
To solve for x, we can multiply both sides of the equation by 7/3 to get:
5x - 80 = (7/3) * x
Now we can simplify and solve for x:
15x - 240 = 7x
15x - 7x = 240
8x = 240
x = 240/8
x = 30
So Sally had $30 originally. Since Ruby had 5 times as much money as Sally, Ruby had:
5x = 5 * 30 = 150
Therefore, Ruby had $150 at first.