A family of 20 purchased tickets to the county fair. Tickets for adults cost $8 while tickets for children cost $4. If the total cost of tickets were $100, how many family members were adults and children? Explain how you solved the problem

There are 5 adults and 15 children in the family.

Step-by-step explanation:

Given

Number of people in the family = 20

Cost of adults tickets = $8

Cost of children tickets = $4

Total ticket sold = $100

Required

How many adults and children are in the family.

Let C represent children and A represent adults.

If there are 20 members of the family, then.

A + C = 20

Also, if adult tickets is sold for $8 and children tickets is sold for $4 and the total cost of tickets were $100, then we have

8A + 4C = 100.

Now, we have two equations to be solved simultaneously.

A + C = 20 --- (1)

8A + 4C = 100 (2)

Make C the subject of formula in (1)

C = 20 - A.

Substituton 20 - A for C in (2)

8A + 4(20 - A) = 100

8A + 80 - 4A = 100

Collect like terms

8A - 4A = 100 - 80

4A = 20

Multiply both sides by ¼

¼ * 4A = ¼ * 20

A = 5

Recall that C = 20 - A

So,

C ,= 20 - 5

C = 15.

Hence, there are 5 adults and 15 children in the family.

The Question was solved by getting an expression to represent the amount of tickets that were sold and another expression for the total number of people in the family.

The two expressions gave us a simultaneous equation and the equations were solved simultaneously.

we know that

applying the law of sines

°

so

∠j=18°

∠k=29°

∠l=180-(18+29)=133°

the answer part a) is

the measure of angle k is  ≈29°

part b)  the measure of angle k could also be

(180-29)=151°

so

∠j=18°

∠k=151°

∠l=180-(18+151)=11°

the answer part b) is

the measure of angle k could also be 151°

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