How much did she start the day with?

Question

Katie met her friend Sarah  for lunch over the weekend.The bus,ride downtown cost $2.She spent half of the money she started the day with on lunch.Then she ran into her friend Dave who paid her the $6 he owed  her.Then Katie  paid to take the bus home.when she arrived home she had $10 left.how much did she start the day with?

Answer 1

Let the amount of Money she started with be x

 

You need to form one equation one unknown with x and solve for it

 

Every amount she paid for let that be s -ve amount and every amount she received be a +ve amount

 

1- She started the day with $x  +$x

1- She paid $2 to take the bus downtown  -$2

2- She paid half what she started the day with for Lunch -$X/2

3- She got back $6 from he friend Dave +$6

4- She took the bus back home and spent another $2 or -$2

 

when she got home she had 10$ left

 

Set up the equation as follows:

 

x-2-(x/2)+6-2=10, solve for x,  x-4-(x/2)+6=10, x+2-(x/2)=10

 

Multiply both sides of the equation with 2 to get rid of the fraction

 

2[x+2-(x/2)=10], 2x+4-x=20, x+4 =20, subtract 4 from both sides

 

x+4-4=20-4, x=16 Check substitute x in the equation

 

16-2-(16/2)+6-2=16-4+6-8=22-12=10 checks,

 

Katie started the day with $16