# On Monday afternoon, the store sold 1/2 of its supply of bottled water. On Tuesday, it sold 5 gallons of water. On Wednesday, it sold 12 gallons.<continued> On...

On Monday afternoon, the store sold 1/2 of its supply of bottled water. On Tuesday, it sold 5 gallons of water. On Wednesday, it sold 12 gallons.

<continued>

On Thursday, the store recieved a 15 gallon shipment. The store then had 22 gallons in stock. How many gallons of water did the store have on Monday morning?

*print*Print*list*Cite

In this problem it could be helpful to work backwards.

If on Thursday the store received 15 gallons which brought them to a total of 22, then 22-15=7 so on Thursday they started out with 7 gallons.

On Tuesday and Wednesday they sold a total of 5+12 = 17 gallons.

This means that on Tuesday morning before they sold any they had 17+7= 24 gallons of water.

If on Monday afternoon they sold half of what they had, then they had twice as much Monday morning as on Tuesday morning. So 24x2=48gallons on Monday morning.

-------------------------------------------

22-15= 7

5+12+7=24

24x2=48

1/2x - 5 - 12 + 15 = 22

Combine like terms

1/2x - 2 = 22

Add 2 to both sides

1/2x = 24

Multiply both sides by 2 to isolate x.

x = 48

Therefore, there were 48 gallons on Monday

Work backwards to solve the entire equation:

First, he left 22 gallons of water in stock, the remainder of water left behind, and they received 15 gallons of water during shipment, so minus 15 from 22 to get 7 so they started with 7 gallons of water on Thursday.

Now for Wednesday, it sold 12 gallons so we add 12 to the 7 gallons he started with on Thursday to get 19 gallins

For Tuesday, do the same thing and add 5 more gallons to get 24 gallons.

Lastly, for Monday, if they had sold half of what they had intially, they would have twice as much they had on Monday than on Tuesday, so multply 24 by 2 to get **48 gallons**.

1/2x - 5 - 12 + 15 = 22

1/2x - 2 = 22

1/2x = 24

x = 48

So, the store had 48 gallons of water on Monday morning.