Mr. Kaplan bought 11 tickets to the circus and spent $50. He bought child tickets for $4 each and bought adult tickets for $7 each. How many child and adult tickets did Mr. Kaplan buy?

9 child and 2 adult

Step-by-step explanation:

We can set up a systems of equations to solve this.

First equation:

We know he spent a total of $50 and child tickets are $4 while adult tickets are $7. We can set up an equation to represent this.

50=4c + 7a

c represents the number of child tickets bought and a represents the number of adult tickets bought.

Second Equation:

We know he bought 11 tickets, some of them are child tickets while others are for adults. We can represent this in an equation.

11= c + a

c represents the number of child tickets bought and a represents the number of adult tickets bought.

Put it all together:

The first step to solve one of the equations, isolating one of the variables. In this explanation, I will be solving the second equation first. I am going to solve it to be in terms of a, meaning I will isolate a.

Now that I have this equation, I will plug it in for a in the first equation and solve to isolate c.

Now we know that the number of child tickets bought was 9. To find out the number of adults tickets bought we plug 9 into another equation. I'm going to plug it into the second equation and solve to isolate a.

Now we are done, we know he bought 2 adult tickets and 9 child tickets.

your exact question is kind of difficult to understand, so maybe an example will explain what you're supposed to do? i'll work through the first problem on the worksheet.

suppose you have a tray of 652 brownies, and you have 5 friends that you want to feed without picking favorites. how many brownies can you dole out to each of your friends in equal amounts? how many will be left over for you to eat?

what you're doing here is finding a way to arrange the number 652 as the sum of integer multiple of 5 and some remainder:

here ("q" for quotient) is the number of brownies each of your friends get, and is the remainder. that's the basic idea behind division.

we break up the number 652 into parts so that the leading digit stands on its own:

652 = 600 + 52

first we check if it's possible to hand out exactly 100 brownies to each friend. with 5 friends, this means we want to know if we can take out 500 brownies from the tray. we can do this 1 time because we have 600 brownies to take from, and when we do that we're left with 100 + 52 brownies to divvy up. so we know that

652 = 1*500 + 152

next we want to know if it's possible to hand out exactly 10 brownies per friend. if we can, we have to remove 50 brownies from the tray each time until we can't. we have 152 brownies left, and we know that 3(50) = 150, so

152 = 3*50 + 2

now we have 2 brownies left in the tray. is it possible to hand 1 out to each of your 5 friends? no, you'd need a minimum of 5 brownies to do that. so the last 2 are yours.

putting everything together, we found that

652 = 1*500 + 3*50 + 2

and we can rearrange this to write

652 = 5*100 + 5*30 + 2

652 = 5(100 + 30) + 2

652 = 5*130 + 2

so and .

you might be more accustomed to the table depicting the algorithm. that's just a compact way of organizing what we've done above. you can consult the image i've attached below.