A charity will give away exactly $600 for tickets for adults and children to attend a concert. The adult tickets are $3.00 each, while each child's ticket costs $2.00. The $600 could be used for 200 adult tickets and no child tickets; it could be used for 300 child tickets and no adult tickets; or some combination of adult and child tickets that adds to a cost of $600; for example, 60 child tickets at a cost of $120 and 160 adult tickets at a cost of $480. However, another restriction exists that limits the number of adult and children tickets: the number of adult tickets must be 200 less than twice the number of child tickets. How many adult tickets and how many child tickets should be purchased to meet these two conditions?

Question
Asked Apr 17, 2019
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A charity will give away exactly $600 for tickets for adults and children to attend a concert. The adult tickets are $3.00 each, while each child's ticket costs $2.00. The $600 could be used for 200 adult tickets and no child tickets; it could be used for 300 child tickets and no adult tickets; or some combination of adult and child tickets that adds to a cost of $600; for example, 60 child tickets at a cost of $120 and 160 adult tickets at a cost of $480. However, another restriction exists that limits the number of adult and children tickets: the number of adult tickets must be 200 less than twice the number of child tickets. How many adult tickets and how many child tickets should be purchased to meet these two conditions?

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Expert Answer

Step 1

to determine the number of tickets in each category meeting all the given constraints

Step 2

Let A and C denote the number of adult and child tickets to be sold . First list  the conditions  on A and C.

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Step 3

Solve A =100 an...

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