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15 Mary had ten pieces of paper. Some of them were squares, and the rest were triangles. She cut three squares diagonally from corner to corner. She then found that the total number of vertices of the 13 pieces of paper was 42 . She had $\qquad$ triangles before making the cuts.

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∻Solution by Steps∻ ‖ step 1 ⋮ Given the equations from the problem: $x + 20 - (y + 20) = 15$ and $x - 5 + y - 5 = 33$. ‖ ‖ step 2 ⋮ Simplify the first equation: $x + 20 - y - 20 = 15 \implies x - y = 15$. ‖ ‖ step 3 ⋮ Simplify the second equation: $x - 5 + y - 5 = 33 \implies x + y - 10 = 33 \implies x + y = 43$. ‖ ‖ step 4 ⋮ Solve the system of equations: $x - y = 15$ and $x + y = 43$. ‖ ‖ step 5 ⋮ Add the two equations: $(x - y) + (x + y) = 15 + 43 \implies 2x = 58 \implies x = 29$. ‖ ‖ step 6 ⋮ Substitute $x = 29$ into $x + y = 43$: $29 + y = 43 \implies y = 14$. ‖ ∻Answer∻ ⚹ $x = 29$ and $y = 14$ ⚹ ∻Key Concept∻ ⚹System of Linear Equations⚹ ∻Explanation∻ ⚹To solve for $x$ and $y$, we used the system of linear equations derived from the problem statement. By simplifying and solving these equations, we found the values of $x$ and $y$.⚹◊What is the total number of vertices of a triangle and a square?⍭ Generate me a similar question◊

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