The Wheel Shop, Level C
Three months later, some vehicles have sold and new models have been brought into the Wheel Shop. Now there
are bicycles, tandem bicycles, and tricycles in the shop. There are a total of 135 seats, 118 front handlebars, and
269 wheels. How many bicycles, tandem bicycles, and tricycles are in the shop?
B: the number of bicycles (that are not tandem)
T: the number of tandem bikes
R: the number of tricycles
http://www.insidemathematics.org/assets/problems-of-the-month/the%20wheel%20shop.pdf
Using Pictures
Using Algebra (System of Equations)
Using Pictures
B
T
B
T
Using Algebra (System of Equations)
𝐵 + 𝑇 + 𝑅 = 118
R
(3)
T
𝐵 + 2𝑇 + 𝑅 = 135
R
(2)
B
(1)
B
T
T
R
R
R
2𝐵 + 2𝑇 + 3𝑅 = 269
𝐵 + 𝑇 + 𝑅 = 118
𝐵 + 𝑇 + 𝑅 + 𝑇 = 135
2(𝐵 + 𝑇 + 𝑅) + 𝑅 = 269
118 + 𝑇 = 135
2(118) + 𝑅 = 269