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Sagot :
Children : 144
Adults : 51
Explanation
Step 1
Set the equations
let
x represents the number of children
y represents the number of adults
charge per child:8
charge per adult:11
total people:195
then
a)the total people is 195, so
[tex]x+y=195\rightarrow equation(1)[/tex]b) the total bill was $1713,so
total childrend +total adults=173
but,
total adults cost= rate*number of adults
total children cost= rate*number of childe
replacing
[tex]8x+11y=1713\rightarrow equation(2)[/tex]Step 2
solve the equations,
[tex]\begin{gathered} x+y=195\rightarrow equation(1) \\ 8x+11y=1713\rightarrow equation(2) \end{gathered}[/tex]a) isolate the x value from equation 81) and replace in eqaution (2)
[tex]\begin{gathered} x+y=195\rightarrow equation(1) \\ \text{subtract y in both sides} \\ x+y-y=195-y \\ x=195-y \end{gathered}[/tex]replace in equation (2)
[tex]\begin{gathered} 8x+11y=1713\rightarrow equation(2) \\ 8(195-y)+11y=1713 \\ 1560-8y+11y=1713 \\ 3y+1560=1713 \\ \text{subtract 1560 in both sides} \\ 3y+1560-1560=1713-1560 \\ 3y=153 \\ \text{divide bothsides by 3} \\ \frac{3y}{3}=\frac{153}{3} \\ y=51 \end{gathered}[/tex]therefore, the number of adults is 51
b) now, replace the y value into equation (1) to find x
[tex]\begin{gathered} x+y=195\rightarrow equation(1) \\ x+51=195 \\ \text{subtract 51 in both sides} \\ x+51-51=195-51 \\ x=144 \end{gathered}[/tex]so, the number of children is 144
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