Degree of graph

Question

There is a simple graph with 65 edges containing vertices of degree 2,3 and 4. In which vertices with degree 3 are twice the number of vertices with degree 4 and there are 10 vertices with degree 2. Number of vertices containing degree 3 and 4 are ___ and __ .

Comments

22 and 11

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22 and 11 , let n = number of vertices of degree 4.

$10*2 + 2n *3 + n*4 = 2*65$

$n = 11$

$2n = 22$

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Sum of degree = $2*$no of edges

Let no of edges with degree $ 4=x$ so no of edges with degree $3=2x$

$10*2+2x*3+x*4= 2*65$

$20+6x+4x=130$

$10x=110$

$x=11$

No of vertices with degree $4= 11$

No of vertices with degree $3= 2x= 22$

Answer 1

sum of degree of vertices= 2*E

10*2+x*4+2x*3=130

so X=11 vertices with degree 4

and  2X=22 vertices with degree 3