how many of each ticket did they sell?

Question

A senior citizen's ticket is $3 and a child ticket is $5. If they made $1450 dollars and sold a total of $350 child and senior citizen tickets.

Answer 1

I'm assuming 350 is the number of total ticket sold.

In this problem X is the number senior citizen tickets and Y is the number of children's tickets.

 

This problem is solving a system of equations

E1: X + Y = 350

E2: 3X + 5Y = 1450

 

rearrange E1 solving for Y

Y = 350 - X

 

plug Y into E2 and solve for X

3X + 5(350- X) = 1450

3X + 1750 - 5X = 1450

                 -2X = -300

                    X = 150

 

Plug X into the orignal E1 to find Y

Y = 350 -150

Y = 200

 

Answer 2

Hello Keia,

 

Let's set this up.

 

S = # senior citizen tickets.

C = # child tickets

 

From the 1st part of the 2nd sentence we have

3S + 5C = 1450

 

I think there's a typo in the latter part of the second sentence.  I think it should be 350 tickets not $350

So

S + C = 350

 

Our system of linear equations is

3S + 5C = 1450
S + C = 350

 

Using elimination to solve we can multiply the 2nd equation by -3

 

3S + 5C = 1450
(S + C = 350) (-3)

 

3S + 5C = 1450
-3S - 3C = -1050

 

Adding these two equations together

2C = 400

C = 200

 

Finally since S+C = 350 and C = 200, then S = 150

 

200 child and 150 senior citizen tickets were sold.