Problem

Create a mixture problem of your own, and solve i…

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Problem 62 Hard Difficulty

Dry mixture problems.
Museum Tours. The ticket prices for the Coca-Cola Museum
in Atlanta are shown. A family purchased 3 more children's
tickets than adult tickets, and 1 less senior ticket than adult
tickets. The total cost of the tickets was $\$ 131 .$ How many of
each type did they purchase?

Answer

The family purchased 3 adult tickets, 6 children's tickets and 2 senior tickets.

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Elementary and Intermediate Algebra

Chapter 2

Equations, Inequalities, and Problem Solving

Section 6

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Video Transcript

problem. 62 creates a ticket. Prices for the Cocoa Cola Museum in Atlanta are shown. Ah, family purchased three more Children's tickets, an adult tickets and one last senior ticket than dull tickets. The total cost of the tickets was $131. How many of each type of the purchase? So I started off by making a chart or a table that has adult senior and child tickets, and I'm using the equation number times values equal to total value. I know that the adult ticket is $15 each, the senior ticket is $13 each, and the child sick. It is $10 each. We don't know the number of tickets for each category that was purchased, but we do know that one less senior ticket was purchased in adults and three more Children's tickets were purchased an adult. So I'm gonna use X represent adult and then X minus once represents Sr and then X plus three to represent the Children sick. It's so find the total Valium and multiply that number times a values for adults. Gonna be 15 x for senior. It's gonna be 13 times X minus one for a child. It's gonna be 10 times X plus three. And then we also know the total. Monta is spent on the tickets, and that's $131 someone ACLU include that in our chart. So 131. And then from here, I'm gonna combine all of the total values for each category of ticket and make it equal to the 131. So I have 15 x plus 13 times X minus one plus 10 times X plus three is equal to 131 From here. I have to distribute 13 to each of the terms inside the parentheses, so 13 times X and 13 times a good one as well as the 10 Times X and then the 10 times in three. So I'm gonna rewrite the equation. We have 15 x plus 13 times x is 13 x 13 times I could've won is negative 13 10 times X is 10 x 10 times three is 30 is equal to 100 and 31. And then from here on in a combined like terms. So we have 15 expose, 13 x plus 10 x, and that is 38 x and then we also have negative 13 plus 30. And that's 17. So we have 38 X plus 17 is equal to 131 and this is a juice up equation. So we have some first get our constant of 17 to the other side. And to do that, we're gonna subtract 17 on each side. Uh huh. 17 minus 17 is zero. So then we have 38. X is equal to ah, 131 minus 17 is 114. And then to get the 38 to the other side, we're gonna have to divide both sides by 38. So 30 eights of out by 38 is one. So that leaves us with X, is equal to, ah, 114 divided by 38 and that is three. So since X represents a number of adult tickets, you know that three adult tickets were purchased and then to figure out how many senior tickets were purchased, we just have to do X minus one. So three minus one is two. So that means that two senior tickets were purchased and then to figure out how many Children's tickets were purchased. We have to do experts three, so that's three plus three and not make six. So we have six Children's tickets and that is our solution.

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