Respuesta :
Answer:
There are 64 adults and 36 children at the local museum.
Step-by-step explanation:
Given,
Total number of people = 100
Total paid amount = $1056
Cost of 1 adult ticket = $12
Cost of 1 child ticket = $8
Solution,
Let the number of child be 'x'.
And also let the number of adult be 'y'.
So, the total number of people is the sum of the number of child and the number of adult.
On framing the above sentence in equation form, we get;
[tex]x+y=100\ \ \ \ equation\ 1[/tex]
Again total paid amount is the sum of the number of child multiplied with cost of 1 child ticket and the number of adult multiplied with cost of 1 adult ticket.
On framing the above sentence in equation form, we get;
[tex]8x+12y=1056\ \ \ \ equation\ 2[/tex]
On multiplying equation 1 by 8, we get;
[tex]8x+8y=800\ \ \ \ equation\ 3[/tex]
Now subtracting equation 3 by equation 2, we get;
[tex](8x+12y)-(8x+8y)=1056-800\\\\8x+12y-8x-8y=256\\\\4y=256\\\\y=\frac{256}{4}=64[/tex]
On substituting the value of 'y' in equation 1, we get;
[tex]x+y=100\\\\x+64=100\\\\x=100-64=36[/tex]
Hence There are 64 adults and 36 children at the local museum.
The number of adults and children in the group can be determined by using an algebraic equation. There are total 100 people paid the an entry fee so sum would be adult and children.
There are 64 adults and 36 children at the local museum
Given:
The entry cost for the adult is [tex]\$12[/tex].
The entry cost for the child is [tex]\$ 8[/tex].
The total entry fee is [tex]\$1056[/tex] .
Let the number of adult is [tex]x[/tex] and number of child is [tex]y[/tex] .
Write the algebraic expression for total number of people.
[tex]\begin{aligned}x+y=100\\x=100-y\\\end{aligned}[/tex]
The total paid amount is the sum of the number of child multiplied by the cost of 1 child cost and the number of adults multiplied by the cost of 1 adult cost.
[tex]8x+12y=1056[/tex]
Substitute [tex](100-y)[/tex] for [tex]x[/tex].
[tex]8(100-y)+12y=1056\\\begin{aligned}800-8y+12y=1056\\4y=1056-800\\4y=256\\y=64\\\end[/tex]
Calculate the value of [tex]x[/tex].
[tex]x=100-64\\x=36[/tex]
Thus, there are 64 adults and 36 children at the local museum.
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