Question

The wood on the back deck of a house needs waterproofing. The shape of the deck
is a rectangle with the length of 40 feet and a width of 3 yards. A gallon can of
waterproof stain covers 50 square feet and costs $19.99 per can plus 8% sales tax.
You go to the hardware store to purchase the waterproof stain needed to complete
the job. You give the cashier $150. How much change do you receive, or how much
additional cash must you find in order to be able to pay for all of the stain you need?
You must show all calculations.
Area of Rectangle = length X width
You cannot split up a can of stain.
You must show all calculations.

Answer 1

Dimensions of a rectangular deck = $40$ feet by $3$ yards

Width of the deck is in yards, so convert it into feet.

Since, $\frac{1}{3}$ yards = 1 foot

Therefore, 1 yard = $3$ feet

And $3$ yards = $3\times 3$ feet

                    = $9$ feet

Therefore, dimensions of the rectangular deck = $40$ feet by $9$ feet

Area of the deck = Length × Width

                            = $40\times 9$

                            = $360$ square feet

∵ $50$ square feet of deck is stained by number of cans = 1

∴ 1 square feet will be stained by number of cans = $\frac{1}{50}$

∴ $360$ square feet will be stained by cans = $\frac{360}{50}$ = $7.2$

We can not purchase can in fractions or parts.

Therefore, number of cans to be purchased = $8$

Cost of waterproof stain per can = $$19.99$ plus $8$% sales tax

Therefore, actual cost of 1 can to be paid for the waterproof stain

= $(19.99 + 19.99\times \frac{8}{100})$

= $19.99+1.5992$

= $$21.5892$

Cost of $8$ cans = $21.5892\times 8$

                         = $$172.71$

I have paid $$150$ to the cashier.

Therefore, additional money to be paid = $172.71-150$

                                                                  = $$22.71$

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