Question 1164695
the pay as you go plan charges 300 dollars plus 5 dollars a foot.
the guaranteed water plan charges a flat fee of 8000 dollars.


let x equal the number of feet of depth that needs to be drilled to get adequate water for a household.


the formula for pay as you go becomes y1 = 300 + 5x.
the guaranteed water plan becomes y2 = 8000.


the pay as you go plan will be cheaper when y1 < y2.
this occurs when 300 + 5x < 8000
subtract 300 from both sides of this inequality to get:
5x < 7700
divide both sides of this inequality by 5 to get:
x < 1540


the pay as you go plan will be cheaper than the guaranteed water plan when the number of feet of depth that has to be drilled is less than 1540.


when the depth is 1539, the pay as you go plan is 300 + 5 * 1539 = 7995.
when the depth is 1540, the pay as you go plan is 300 + 5 * 1540 = 8000.
when the depth is 1541, the pay as you go plan is 300 + 5 * 1541 = 8005.


you can see that the pay as you go plan is cheaper when the depth is less than 1540.