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Welcome to Brainfuse!

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In the last lesson we found the concentration of a substance in a solution.

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In this lesson will work with another common type of mixture problem.

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Here it is on screen,

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And I'll paste those formulas on as a reference as well.

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Here are our formulas and just to be clear these are both two versions of the same formula.

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We have the product of a mixture, that's our amount, and it's the product of an initial quantity

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Times a rate. We've already worked with a substance we just worked with caffeine.

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Now we'll move to money. Let's read the problem.

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A museum charges students $10 for a ticket while non-students need to pay $25 per ticket.

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This museum earned $8,250 from ticket sales on the opening weekend

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Of its new exhibit.

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If there were three times more tickets sold to students than non-students, how many students bought tickets?

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So we need to use this equation to find how many students bought tickets.

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We know that the museum earned

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$8,250

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So the amount earned

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Is equal to $8,250

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And we know that the museum charges students $10 for a ticket

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So that would be the rate for students, put R-sub-s.

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R-sub-s equals $10 per ticket, or "tkt" to save some time,

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And non-students, they need to pay $25 per ticket.

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So we'll let non-students be represented by R-sub-n, which equals $25 per ticket.

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What else do we know?

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We know that

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There were three times more tickets sold to students

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So the number of tickets sold to students, T-sub-s, equals three times the number of tickets

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Sold to non-students, T-sub-n.

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So let's use these values to set up an equation. Amount earned: $8,250.

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Equals

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We'll start with the students. That would be number of tickets sold,

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That's 3 x T-sub-n, and that would be

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Tickets

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Times $10 per ticket

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And then they need to add in the sales from the non-students,

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That would be

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T-sub-n tickets,

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Times $25 per ticket.

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All right, let's do the math.

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Starting with the students,

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Tickets, as a unit, cancels out, leaving us with 3(T-sub-n) times $10.

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So that would be 30

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T-sub-n

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Dollars

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30 x T-sub-n, plus

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Again

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Tickets cancels out, and we're left with $25

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Times T-sub-n.

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We can now add like terms,

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So 30 + 25

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Is equal to 55.

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That would be $55 times T-sub-n,

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And we can solve for T-sub-n.

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To solve for T-n, we can divide both sides

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By $55

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Cancels out on the right,

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And we're left with

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$8,250 divided by $55

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And that is equal to

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150.

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This tells us that there were 150 tickets sold to non-adults.

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But is that our answer?

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We're supposed to find how many students bought tickets.

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To do that,

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We can use this equation for T-s.

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T-s equals

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Three times T-n,

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And T-n we found is equal to 150.

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That is equal to 450. Move this up a bit.

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To answer the question, if everyone was honest, there were 450 students

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Who bought tickets.

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For more practice with mixture problems you can log on to Live Help

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And work with a Brainfuse tutor.

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And thanks for watching this lesson.