Question

A very large bucket is filled with sand, and sand weighs 13 13 pounds per gallon. When the bucket contains 3 3 gallons of sand, the combined weight of the bucket and sand is 43.4 43.4 pounds. Which of the following formulas expresses the combined weight of the bucket and sand in pounds, w w, in terms of the number of gallons of sand in the tank, v v?

a. w = 13(v - 55.5) + 4 = 13v + 4
b. w = 13v + 55.5
c. w = 13v
d. w = 13(v – 4) + 55.5

Answer 1

w = 13 * (v - 3) + 43.4

Explanation:

We have to density of sand = d = 13 pounds per gallon

Number of gallons of sand in the bucket = v

Combined weight of bucket and sand = w

Now we have to "x" be the weight of bucket then as per the question,

43.4 = x + 3 * d

x = 43.4 - 3 * d

x = 43.4 - 3 * 13

Now w is the same:

w = d * v + x =

w = 13 * v + 43.4 - 3 * 13

common factor 13, and we are left with:

w = 13 * (v - 3) + 43.4

the answers do not match the values given in the problem, but the structure is that of option d.