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Threc-E Gifths = of the students of & class make satisfactory progress math. If 70 DO NOT make satisfactory progress; how many students are there in the class? ...

Question

Threc-E Gifths = of the students of & class make satisfactory progress math. If 70 DO NOT make satisfactory progress; how many students are there in the class? [40 pts]b) At benefit concert; 600 tickets were sold and S1SOO was raised. If there were $2 and $5 ticket; how MuI each kind were sold?

Threc-E Gifths = of the students of & class make satisfactory progress math. If 70 DO NOT make satisfactory progress; how many students are there in the class? [40 pts] b) At benefit concert; 600 tickets were sold and S1SOO was raised. If there were $2 and $5 ticket; how MuI each kind were sold?



Answers

In the following exercises, translate to a system of equations and solve. Tickets for a show are $\$ 70$ for adults and $\$ 50$ for children. One evening performance had a total of 300 tickets sold and the receipts totaled \$17,200. How many adult and how many child tickets were sold?

So I have 800 tickets were sold to a movie. 480 of those were sold at full price of $7 and I had gate receipts totalling $4960. My goal is to figure out the cost of a student ticket. So since this is what I don't know, that's going to be X. So the cost of a full price ticket or the amount of money taken in from full price tickets were $7 times 480 Although it doesn't give it to me directly. I know the number of student tickets has to be the total minus the number of full priced tickets. So 800 minus 4 80 is 3 20 and the cost of those idea of each one of those I don't know. But that's X. So here's the total cost for a full price. Here's the total cost for students, and that has to equal 4960. Now I can go ahead and simplify and solve for X, so I'm going to start by doing seven times 480 which is 3360 plus 3 20 x and that's got equal 49 60. I'm going to subtract 33 60 from both sides. My goal now is to get the X by itself. That leaves May 3 20. X equals 1600. Now I'm gonna go ahead and a viable sides by 3 20 Divide by 3 20 and that's going to give me an X equal to Let's put them your calculator by 3 20 That's going to give me an X equal to five, so the cost of a student ticket is $5.

But so if we're selling good seats and cheap seeds and there was 900 altogether, then we can say that axe is equal to the number of good seeds. Jesus, using X to count the number of good seats any very well work. So we have a total of 900 seats sold. The 900 minus X will be the number of seats left over which, in this case, we're calling chief seats. So the number of cheap seats and together they would add to 900. Okay, so we also know that the good seats cost $20. So we have $20 times the number of good seats, which is X Hopes. Right? The $30 could see each other once, but something that yes, um, and the chief seats or trade all are so plus $20 times number cheat seats, which is 900 uh, my sex wreck. It's then that equals how much money we made, which was $25,000. We can use this equation, which is a quadratic equation to solve for how many seats of each type result. So we're just gonna start by organizing our former the and simplifying outlets were multiplying into the brackets and subtract 2,505,000 to the sides. It's one of 30 x plus. So then we're 20 times 900. It was just 18,000 minus 20 x, and they moved the 25,000 to the outside. So minus 25,000. Now give us equals zero, which will allow us to solve eventually. Let's keep going. Um, so 30 X minus 20 acts would be 10 access and then 18,000 positive minus 25,000. Move. My seven does'nt. It was there. So this isn't actually 1/4 question because we don't have an X squared. So we're gonna just solve this like we would any leader. Your question. And I'm going to add $7000 to a science or 7002 ascents. The's council. We get 10 X equal 7000 your Bible science by 10 and we get X equal 700. So that means we sold 700 good seats since we had 900 seats altogether. Then very quickly do the math over here. Just to see it 900 by a 700 would leave us with 200 cheap seats left over. So we have 200 cheek seats now. We're done

So I have some information about tickets to a college basketball game. Ah, full price ticket is to 50 and a student ticket is a dollar 75. At this particulary game, I sold 585 tickets and I made a total of $1217.25. And my goal here is to figure out how many student tickets were sold. So I need to define a variable and use this information to write an equation. So my student ticket, I'm going to go ahead and define as I sold ex of them because that's what I'm trying to find. If I sold ex student tickets, then I sold 585 minus X tickets at full price. Now I know from my student tickets I made a dollar 75 times the number of tickets. And for my full price ticket, I made 2.5 times the number of tickets 5 85 minus X. These two amounts have to add together to give me the total amount of money that was taken in. So now that I have an equation, I can go ahead and solve four x So let's go ahead and distribute the 2.5 to make the parentheses go away. 2.5 times 5 85 So that's 1.75 x plus 1462.5 minus 2.5 x equals 1000 to 17.25 No, I'm gonna go ahead and do two steps again. I'm going to subtract 1462.5 from both sides 62.5. And when I simplify this, I'm gonna go ahead and combine my life terms at the same time. So 1.75 x minus 2.5 x is minus 0.75 x in 2017.25 minus 14. 62.5 Can do that in my calculator is minus 2 45 0.25 Now immediate the X by itself, which I can do by just dividing by negative 0.75 Divide by negative 0.75 and that's going to give me an X equal to negative divided by negative is positive, so I don't have to worry about that. So to 45.25 divided by 0.75 is 327 and that is my number of students. Tickets sold

We have. The tickets are for Children, is one student is 1.5 and adult is too on let X bite and they said, be the respective numbers off them attended in a particular day where 800 tickets are taught, Salt said. For an amount off 1015 then we can write the given information as the total number of tickets equal to X plus y plus zit equal to 800. And the total amount collected is X plus 1.5 y less twos that equal to you. 1050. We have two equation and three unknowns, so we have two soldiers with the help off any other given information. The next given information is the number off. It's our Children, is three times the adult that is X equal toe three is it three times is that we can subdued in equations both the equations and make these equations it pair off linear equations that does substituting executed, he said. We'll give us to integration. That is for a set place. Why equals 800 and fives that plus 1.5 you called toe 1050. Then we can make this creations so horrible by multiplying to simplify this so this can be converted into one is multiplied with three and two is multiplied with two that will give us new creations. 12 is it plus three y equals 2400 and tennis it plus three. Three y equal 2100. So solving this, they will obtain the value off. Let us said it will do 300 by two, which is equal to 1 50. That is the number off adult. Andi. We have X equal to trees. It that is three times when 50 is the number off Children ages 4 50 Children. Andi Using our first situation you have, we can find why why equal to 800 minus X minus y, which is equal to 200. That is the number off students attended. So this is our answers answers.


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