There are total 71 number of cartoons of belts.
What is linear equation?
A linear equation is an equation in which the highest power of the variable is always 1.
What is substitution method?
The substitution method is the algebraic method to solve simultaneous linear equations. In this method, the value of one variable from one equation is substituted in the other equation.
Let x denotes the number cartoons of belt and y denotes the number cartoon of shoes.
According to the question.
[tex]160x + 465y = 19265[/tex]
The above linear equation can be written as
[tex]32x+93y = 3853..(i)[/tex]
Also,
[tex]x + y = 88[/tex]
⇒ [tex]x = 88 - y[/tex]
Substitute the value of x in equation (i)
[tex]32(88-y)+93y = 3853[/tex]
⇒ [tex]2816-32y + 93y = 3853[/tex]
⇒ [tex]2816 +61y = 3853[/tex]
⇒ [tex]61y = 3853 -2816[/tex]
⇒[tex]61y = 1037[/tex]
⇒ [tex]y = \frac{1037}{61}[/tex]
⇒ [tex]y = 17[/tex]
Therefore,
[tex]x = 88-17 = 71[/tex]
Hence, there are total 71 number of cartoons of belts.
Find out more information about linear equation and substitution method here:
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