Christopher sold tickets to the game hood seats were $5 each and poor seats cost $2 each. 210 people attended and paid $660 how many poor seats were sold

Answer 1

You can rewrite this word problem into two equations [also known as a system of equations]

Let h = hood seats and p = poor seats

Let's start with the money:

You get $5 of hood seats and $2 of poor seats and total equals $660

So the equation for that is: 5h + 2p = 660

Next the number of people attending:

The total number of people attending equals the number of people in hood seats and poor seats

So the equation for that is: h + p = 210

Let's look at the equations together:

5h + 2p = 660

h + p = 210

Let's rewrite the second equation and plug it into the first one:

h + p = 210 => h = 210 - p

5(210 - p) + 2p = 660

Now solve for p:

1050 - 5p +2p = 660

1050 - 3p = 660

1050 - 660 = 3p

390 = 3p

130 = p

Answer: 130 poor seats were sold

Now if you want to find h, just plug it back into either equation and solve:

5h + 2p = 660

5h + 2(130) = 660

5h = 660 - 260

5h = 400

h = 80

Alternatively:

h + p = 210

h + 130 = 210

h = 210 - 130

h = 80

Answer 2

Christopher sold tickets to the game. Good seats were $5 each, and poor seats cost $2 each. 210 people attended and paid $660. How many poor seats were sold?

The trick is to translate this problem that is written in English into a math problem, using numbers and other mathematical symbols.

First, we need to identify and define the unknown terms.

P: # of poor seats sold

G: # of good seats sold

P + G = 210 {210 is the total number of seats sold}

2P + 5G = 660 {the 2, 5, and 660 refer to amounts of dollars}

We now have two equations in two unknowns, which we should be able to solve. Let's solve the first equation for G, and then substitute the value of G into the second equation so that we have will have a single equation with only P as the unknown; P represents the number for which we are looking: the number of poor seats sold.

P + G = 210

P – P + G = 210 – P

G = 210 – P

2P + 5G = 660

2P + 5(210 – P) = 660

2P + 1050 – 5P = 660

–3P + 1050 = 660

–3P + 1050 – 1050 = 660 – 1050

–3P = –390

P = 130

Answer word problems with complete sentences:130 poor seats were sold.