First, we are going to convert the thick of the block from inches to feet. To do that we are going to take advantage of the fact that 1 foot=12 inches to create a multiplier:
[tex]6in* \frac{1ft}{12in} =0.5ft[/tex]
Since the thickens of the wall will be equal to the thickness of each block, the thick of the all is 0.5 feet.
Now, to find the volume of the wall, we are going to use the formula:
[tex]V_{w}=hlt[/tex]
where
[tex]V_{w}[/tex] is the volume of the wall
[tex]h[/tex] is the height of the wall
[tex]l[/tex] is the length of the wall
[tex]t[/tex] is the thickness of the wall
We know for our problem that the wall is 7ft. tall by 20 ft. long, so [tex]h=7ft[/tex] and [tex]l=20ft[/tex]. We also know from our previous calculation that the thickness of the wall is 0.5ft, so [tex]t=0.5ft[/tex]. Lets replace those values in our formula:
[tex]V_{w}=hlt[/tex]
[tex]V_{w}=(7ft)(20ft)(0.5ft)=70ft^3[/tex]
Now we know that the volume of the wall is 70 cubic feet. We also know that 10 blocks are needed for 1 cubic foot, so to find the total numbers of blocks needed, we are going to multiply the volume of the wall by the number of blocks needed for 1 cubic foot:
[tex]TotalBlocks=70ft^3* \frac{10blocks}{1ft^3 } =700 blocks [/tex]
Finally, to find the total cost, we are going to multiply the number of blocks needed by the cost of 1000 blocks:
[tex]TotalCost=700blocks* \frac{75}{1000} =52.5[/tex]
We can conclude that the cost of the wall will be $52.5
