Question

Christian sold tickets to the game. Good seats were $5 each and poor seats cost $2 each. 210 people attended and paid $660. Write a system of linear equations that can be used to find how many good seats (g) and How many poor seats (p) were sold.

Answer 1

Let g represent the # of good seats and p the # of poor ones.

Then g + p = 210 seats. Then p = 210 - g.

Revenue: ($5)g + ($2)p = $660. Substituting 210 - g for p,

($5)g + ($2)(210 - g) = $660

Simplifying, 5g + 420 - 2g = 660 => 3g = 240 => g = 80

Then there were 80 good seats and (210-80), or 130, poor seats.

Answer 2

Answer with Step-by-step explanation:

Let g denotes number of good seats sold

and p denotes number of poor seats poor seats sold.

Good seats were $5 each and poor seats cost $2 each.

Total 210 people attended

i.e. g+p=210 -----(1)

Total amount=$660

i.e. 5g+2p=660 ------(2)

equation (2)-2×(1) gives:

5g+2p-(2g+2p)=660-420

i.e. 3g=240

Dividing both sides by 3 gives

g=80

Putting value of g in equation (1) gives:

80+p=210

p=210-80

i.e. p=130

Hence, Number of good seats sold=80

Number of poor seats sold=130