Word problem with money amounts

Question

admission to a museum is $5.00 for adults and 3.00$ for children. In one day 2,400$ was collected for 620 paid admissions. How many adults and how many children paid to visit the museum that day? 

Answer 1

First thing, is to write equations for the information given in the problem...

Let x=adults, y=children

5x+3y=2400

x+y=620

Rearrange the second equation to solve for one of the variables...

y=620-x

Then plug this formula into the first equation and solve for x.

5x+3y=2400

5x+3(620-x)=2400

5x+1860-3x=2400

2x=540

x=270

then plug this value back into one of the original equations to solve for the other variable.

x+y=620

270+y=620

y=350

 

So, there were 270 adults and 350 children that visited the museum that day.

 

Hope this helps,

chris

Answer 2

Lets call the number of adults who visited the museum, x, and the number of children who visited the museum, y.

 

We know that there were 620 paid admissions. We can write our first equation:

x + y = 620   (this says the number of adults and children who visited that day totaled 620) --- equation (1)

 

 

We know the price times the number of tickets sold can give us the revenue. We also know a total of $2400 was collected that day:

 

5x + 3y = 2400 ---- equation (2)

 

 

We can rewrite (1) as: x = 620 - y  and plug this new equation into (2):

5x + 3y =2400

5 (620 - y) + 3y = 2400

3100 - 5 y + 3y = 2400

-2 y = 2400 -3100 = -700

2y = 700

y =350

 

x = 620 - 350 = 270

 

Let's check our answers: 270 * 5 + 350 *3 = 1350 + 1050 = 2400