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Combinatorics Difficulty 2.0 Junior Find the answer United Kingdom

In the window of Bradley's Bicycle Bazaar there are some unicycles, some bicycles and some tricycles. Laura sees that there are seven saddles in total, thirteen wheels in total and more bicycles than tricycles. How many unicycles are in the window?

(A) $1$ (B) $2$ (C) $3$ (D) $4$ (E) $5$

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Source: UK Mathematics Trust, licensed © UK Mathematics Trust; past papers published free at ukmt.org.uk. Statement reproduced verbatim; metadata (topic, difficulty) added by this project. Solutions are the publisher's, linked not copied.