Question

the tickets for a benefit concert were $6 for friday night and $8 for Saturday night. the total attendence for the two nights was 1090 people. if the total receipts for the two nights were 7856 how many people attended each night

Answer 1

432 people on Friday and 658 on Saturday

Explanation:

Lets use variables for each day

x=Friday and y=Saturday

now write two equations since you were given two different information (money and people)

$6 on Friday and $8 on Saturday with a total amount of $7856

the equation will be 6x+8y=7856

now the second equation will be for people

x amount of people on Friday and y amount of people on saturday for a total of 1090; the equation will be

x+y=1090

put them together

6x+8y=7856

x+y=1090

now you can cancel a variable but manipulating one of the equations. We'll use x, to cancel x you need make it zero so multiply the bottom by -6

6x+8y=7856

-6(x+y=1090)

6x+8y=7856 now subtract downwards, with the x cancelling

-6x-6y=-6540

2y=1316 simplify

(2y/2)=(1316/2)

y=658

insert y into x+y=1090

x+(658)=1090

-658 -658

x=432