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?
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