Question

Tickets to the museum cost $18 for adults and $12 for children. A group of 20 people went to the museum, and the tickets cost $324. The system of equations models this situation, where x is the number of adults and y is the number of children.

x+y=20
18x+12y=324


How many adults and how many children were in the group?

A.
8 adults and 12 children

B.
10 adults and 10 children

C.
12 adults and 8 children

D.
14 adults and 6 children

Answer 1

\(\Large x+y=20\)
solve for y
then plug the equation for y into this equation
\(\Large 18x+12\color{red}y=324\)

Answer 2

Clear? :)

Answer 3

i'm solving the systems of equation by using substitution

Answer 4

okay

Answer 5

to know how many adults \(\color {red}y\) and how many children \(\color{blue} x\) were in the group of 20 people, we must combine the two equations by using the systems of equation as the direction states. I chose doing substitution because it's more understanding. You know how to solve by substitution?

Answer 6

\(\large Step:1\)
\(\color{blue} x+\color{red}y=20\)
solve for \(\color{red}y\)

Answer 7

okay

Answer 8

so how do i do what plz help me

Answer 9

\(\Large \color{blue}x+\color{red}y=20\)
subtract x to both sides
\(\Large \color{blue}{x-x}+\color{red}{y}=20-\color{blue}{x}\)
you'll end up with
\(\Large\color{red}y=20-\color{blue}x\)

Answer 10

plug \(\color{red} y\) which is \(20-\color{blue}{x}\) to y in the equation \(\large 18x+12\color{red}y=324\)

Answer 11

\(\Large 18x+12(20-\color{blue}x)=324\)
clear?

Answer 12

yes

Answer 13

Can you solve for x?
Like, distributing and combining like terms?
\(\Large 18x+\color{red}{12(20-x)}=324\)
distribute the red shaded color, you know how to do that?

Answer 14

no

Answer 15

solve for x in this case, x represents how many adults went to the museum

Answer 16

\(\Large 18x+240-12x=324\)