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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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Answer from Sia

Posted about 2 months ago

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 $y$.

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