can someone help me with number 19 please?

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09-02-2015
Mathematics

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can someone help me with number 19 please?

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AL2006 AL2006 · Answer 1 · 2015-02-09T18:31:08-05:00

I think I can.
Let's do it together:

Let's call the number of buses 'B', and the number of vans 'V'.
(Pretty clever so far, don't you think ?)

OK. What do we know ?

-- Each bus holds 51 passengers. The number of passengers in 'B' buses is 51B.

-- A van holds 10 passengers. The number of passengers in 'V' vans is 10V.

-- The total number of passengers ... (51B + 10V) ... is 142.

-- The total number of vehicles ... (B + V) ... is 6, because there are 6 drivers.

Can you make a system of equations out of that information yet ?
How about this:

   51B + 10V = 142
   B + V =     6

I really think you can handle it from here.
=======================================

Multiply the 2nd equation by 10 :

   51B + 10V = 142
   10B + 10V =   60

Subtract the 2nd equation from the 1st one:

   41B = 82

Divide each side by 41: B = 2 buses

2 buses . . . . 2 drivers . . . . 2 x 51 = 102 passengers

4 vans . . . . . 4 drivers . . . . . 4 x 10 = 40 passengers

6 vehicles . . . 6 drivers . . . . . 102 + 40 = 142 passengers