Truck Deliveries, Math Problem?
Brock's Discount TV has three types of television sets on sale: a 13-in. portable, a 27-in. remote, and a 50-in. console. They have three types of vehicles to use for delivery: vans, small trucks, and large trucks. The vans can carry 8 portable, 3 remote, and 2 console TVs; the small trucks, 15 portable, 10 remote, and 6 console TVs; the large trucks, 22 portable, 20 remote, and 5 console TVs. On a given day of the sale they have 115 portable, 85 remote, and 35 console TVs to deliver. How many vehicles of each type are needed to deliver the TVs?
I'm sorry to ask questions on so many dang word problems, but I have no idea what to do with this one. The answers in the back of the book is:
2 vans, 4 small trucks, and 3 large trucks.
Update:ohh, sorry, thanks
Comments
v = no of vans
s = small trucks
L = large trucks
115 = 8v + 15s + 22L
85 = 3v + 10s + 20L
35 = 2v + 6s + 5L
Solve simultaneously to get..
v = 1.77
s = 3.30
L = 2.34
You have to round them UP in order to be sure of meeting the requirements. Then you get your a nswer.
The answer in the back of the book is in fact wrong!
Work out the total carrying capacity of 2 vans, 4 small trucks and just 2 large trucks.
Portables = 2*8 + 4*15 + 2*22 = 120
Remotes = 2*3 + 4*10 + 2*20 = 86
Consoles = 2*2 + 4*6 + 2*5 = 38
This is more than enough for the required number of all three types of TV on that day.
Alternatively if you used 3 large trucks then you would only need 4 small trucks and no vans or 3 small trucks and 1 van.
It shows that you do not always need to round up ALL of the exact answers to solving the equations. You need to examine all integer solutions nearby.
However, which of these is the best answer? Who is to say? You really need extra information; most likely would be the cost of operating each type of vehicle and driver for a day.
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