Question 878397
On Wednesday there were no tandem bikes in the shop. There were only bicycles and tricycles. There are a total of 24 seats and 61 wheels in the shop. How many bicycles and how many tricycles are in the shop?
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Two ways to do it: (1) without using algebra and (2) using algebra.

(1) Without algebra:

24x2=48, 61-48=13 tricycles, 24-13=11 bicycles

Explanation:

There are 24 seats, so there are 24 vehicles.
If they were all bicycles, there would be only
24x2=48 wheels.  However there are 61 wheels, 
so the extra 61-48 or 13 wheels must belong to
the tricycles.  So there are 13 tricycles and 
24-13=11 bicycles.

(2) using algebra:

 B +  T = 24
2B + 3T = 61

Solve the first equation for T

                T = 24 - B

Substitute (24-B) for B in

          2B + 3T = 61
     2B + 3(24-B) = 61
     2B + 72 - 3B = 61
          -B + 72 = 61
               -B = -11
                B = 11   


Substitute B = 11 in

                T = 24 - B
                T = 24 - 11
                T = 13
 
Edwin</pre>