Question

Bottled water and medical supplies are to be shipped to victims of a hurricane by plane. Eachplane can carry 90,000 pounds and a total volume of 6000 cubic feet. The bottled water weighs20 pounds per container and measures 1 cubic foot. The medical kits each weigh 10 pounds andmeasure 2 cubic feet. How many containers of bottled water and how many medical kits can besent on each plane?solve algebraically and linear systemsstep by step explanation having trouble forming a pattern for word problem solving

Answer 1

Let the number of bottled water be x and number of medical kits be y.

It is given that the bottled water weighs 20 pounds per container and measures 1 cubic foot and the medical kits each weigh 10 pounds and measure 2 cubic feet.

Also the plane can carry 90000 pounds so it follows:

`\begin{gathered} 20x+10y=90000 \\ 2x+y=9000\ldots(i) \end{gathered}`

The plane can carry 6000 cubic feet so it follows:

`x+2y=6000\ldots(ii)`

Multiply equation (i) by -2 to get:

`-4x-2y=-18000\ldots(iii)`

Add (ii) and (iii) to get:

`\begin{gathered} x-4x=6000-18000 \\ -3x=-12000 \\ x=(-12000)/(-3) \\ x=4000 \end{gathered}`

Substitute the value x=4000 in (i) to get:

`\begin{gathered} x+2y=6000 \\ 4000+2y=6000 \\ 2y=6000-4000 \\ 2y=2000 \\ y=(2000)/(2) \\ y=1000 \end{gathered}`

Hence each plane can carry 4000 bottled water and 1000 medical kits.