A delivery truck can transport packages weighing at most 3,800 pounds(lbs) and with a volume of no more than 400 cubic feet (ft^3). The truck transports only two sizes of packages: A small package weighing 30 lbs with a volume of 4ft^3 and a large package weighing 65 lbs with a volume of 9ft^3. Let x represent the number of small packages and y represent the number of large packages. Which system of inequalities describes the possible numbers of packages the truck can transport at one time?A. 6x+13y≥760 and 4x+9y≥ 400B. 6x+ 13y ≤ 760 and 4x+9y≤400C. 15x+2y≤ 1,900 and 65x + 9y≤ 400D. 15x +12y≥ 1,900 and 65x+9y≥ 400
Accepted Solution
A:
Let's approach this problem by slowly eliminating choices.
First consider the keyword "at most" and "no more than". This means that the inequality should be less than or equal to the constant value stated. This will automatically eliminate two choices with the greater than symbol favoring the variables - choices A and D.
Next we associate the right constants to the right coefficients of variables. The two kinds of weight the truck transports are 30 and 65 lbs, and we know that this should not exceed 3,800 lbs. This is therefore our first inequality. The other inequality is for the volume. The combinations of the two volumes 4 and 9 cubic feet should not exceed 400 cubic feet when transported.
If you try to construct the inequality and miss it among the choices, don't worry! Let's try doing some simplifications first and see if it matches either B or C.
After simplification you can get [tex]6x+13y \leq 760[/tex] from dividing the equation by 5 and [tex]4x+9y \leq 400[/tex] for leaving it as it is.
Looking carefully, we can see that this is equivalent to option B.