Answer:
[tex] \boxed{\sf Total \ number \ of \ boys = 16} [/tex]
Given:
Total number of boys and girls in class = 42
Total number of girls = 10 more than the boys
To Find:
Total number of boys
Step-by-step explanation:
Let total number of boys be 'x'
[tex]\sf So, \\ \sf Total \: number \ of \ girls = x + 10 \\ \\ \therefore \\ \sf \implies Total \: number \: of \: boys \: and \: girls \\ \sf \: \: \: \: \: \: \: \: \: \: \: \: \: = Total \: number \: of \: boys + Total \\ \sf \: \: \: \: \: \: \: \: \: \: \: \: \: number \: of \: girls \\ \\ \sf \implies 42 = x + (x + 10) \\ \\ \sf 42 = x + (x + 10) \: is \: equivalent \: to \: x + (x + 10) = 42 : \\ \sf \implies x + (x + 10 )= 42 \\ \sf \implies x + x + 10 = 42 \\ \\ \sf x + x = 2x : \\ \sf \implies \boxed{ \sf 2x} + 10 = 42 [/tex]
[tex] \sf Substrate \: 10 \: from \: both \: sides : \\ \sf \implies 2x + (10 - \boxed{ \sf 10}) = 42 - \boxed{ \sf 10} \\ \\ \sf 10 - 10 = 0 : \\ \sf \implies 2x = 42 - 10 \\ \\ \sf 42 - 10 = 32 : \\ \sf \implies 2x = \boxed{ \sf 32} \\ \\ \sf Divide \: both \ sides \: by \: 2 : \\ \sf \implies \frac{2x}{ \boxed{ \sf 2}} = \frac{32}{ \boxed{ \sf 2}} \\ \\ \sf \frac{2x}{2} = \frac{ \cancel{2}}{ \cancel{2}} \times (x) = x : \\ \sf \implies x = \frac{32}{2} \\ \\ \sf \frac{32}{2} = \frac{16 \times \cancel{2}}{ \cancel{2}} = 16 : \\ \sf \implies x = 16[/tex]
So,
Total number of boys = x = 16
