On opening night of the drama clubs play they made $1366. they sold a total of 199 tickets. they charged $8.50 for each adult ticket and $5.00 for each child's ticket. write a system of equations that can be used to find the number of adult tickets and the number of children's tickets sold.

a+c=199...equation 1

8.5 a+5 c=1,366...equation 2

The number of adults tickets sold=106

The number of children tickets sold=93

Step-by-step explanation:

a). Determine first expression

Let the number of each group be as follows;

adults=a

children=c

total number of people=199

This can be expressed as;

number of people=number of children+number of adults

replacing;

a+c=199...equation 1

b). Determine the second expression

Let the total amount made by the opening night can be expressed as shown;

total amount=(price per child ticket×number of children)+(price per adult ticket×number of adults)

where;

total amount=$1,366

price per child ticket=$5

number of children=c

cost per adult=$8.5

number of adults=a

replacing;

(8.5×a)+(5×c)=1,366

8.5 a+5 c=1,366...equation 2

c). Combine equation 1 and 2 and solve simultaneously

1(8.5 a+5 c=1,366)

-

5(a+c=199)=5 a+5 c=995

(8.5 a-5 a)+(5 c-5 c)=(1,366-995)

3.5 a=371

a=371/3.5

a=106

replacing the value for a in equation 1

106+c=199

c=199-106=93

The number of adults tickets sold=106

The number of children tickets sold=93

answer: 59

step-by-step explanation:

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