Question

Ann had 20$ less than beth. If an spent 3/4 of her money and beth spent 4/5 of her money, ann's remainder would be 5/6 of beth's reaminder, if ann has x$ how much does ann have. make equation and solve it

Answer 1

Answer:

Ann had 40 $ at the start and Beth had 60 $ at the start and Ann spent 30 $ and Beth spent 48 $ .

Step-by-step explanation:

let Ann have x $

Then Beth has x + 20 $

The amount Ann spent = 3/4 ( x) = 3x/4  $

The amount Beth spent = 4/5 ( x + 20) = 4x/5 + 16 = ( 4x + 80 ) /5   $

Ann,s remainder = x - ( 3x/4)

Beth,s remainder = ( x+ 20 ) - ( ( 4x + 80 ) /5 )

Then the equation is -

Ann,s remainder = 5/6 ( Beth,s remainder)

so,  x- ( 3x/4 ) =  5/6 ( ( x+ 20 ) - ( 4x + 80 ) /5 ) )

= ( 4x - 3x) / 4 =  5/6 ( (5(x+ 20)  - 4x  - 80) /5 )

= x/4 = 5/6 ( (5x + 100 - 4x - 80) / 5 )

= x/4 = 5/6 ( x + 20) /5 )

=  x/4 / 5/6 = ( x + 20 ) / 5

=  x/4 x 6/5 = (x + 20)  /5

= 6x/20 = ( x + 20 ) / 5

= 3x//10 = ( x + 20 ) / 5

= 5 ( 3x) = 10 ( x + 20 )

= 15x = 10 x + 200

= 15x - 10x = 200

= 5x = 200

= x = 200/5

= x = 40 $ , which we considered  the amount that Ann had at first

now Beth had x + 20 $ which means Beth had 60 $ .

The money Ann spent = 3/4 x 40 = 30 $ , and she was left with 10 $

The money that Beth spent = 4/5 x 60 $ = 48 $ , and she was left with 12 $