Please solve in correct equation format. If I sell 9 childrens tickets and 9 senior citizen tickets totally $225. How much is a senior and how much is a childs.

Question

Sue is selling tickets. The first day she sold 4 senior citizens and 2 childrens tickets for a total of $80. The 2nd day she received $145 for 5 senior tickets and 7 children's tickets. What is the price of a child's ticket and a senior ticket. Show problem using correct mathematical symbols.

Answer 1

let s=  cost of senior tickets and c=cost of children tickets

 

2 children and 4 senior tickets sold for $80 :  2c + 4s=80 this equation can be reduce to c + 2s = 40 by dividing all through by 2

7 children and 5 senior tickets sold for $145: 7c + 5s=145

 

your  2 equations are below and you can either use the substitution or elimination method to solve for c and s   

c + 2s=40......equation 1

7c + 5s=145....equation 2

 

using the elimination method

 

7(c + 2s=40) =    7c + 14s = 280
-1(7c + 5s=145)= -7c - 5s = -145

 subtract                     9s = 135

 divide                       s=15

 substitute s=15 into equation 1; c +2(15)=40

                                                 c+30=40

subtract 30 from both sides          c=10

                                               

therefore;

senior tickets cost $15 and children tickets cost $10

 

 

Proof

 

9s + 9c =225

9(15) + 9(10) = 135 + 90=225

 

Answer 2

1) Setup an equation for each day. 

 

4s + 2c = 80

5s + 7c = 145

 

2) isolate a variable.

 

2c = 80 -4s

c = 40 -2s

 

3) Plug into the other eq

 

5s + 7(40-2s) = 145

5s + 280 -14s = 145

-9s = -135

s = 15

 

4) Solve for c.

 

c = 40 - 2(15)

c = 10

 

5) Check your work by plugging back into both equations.

 

4(15) + 2(10) = 80

60+20 = 80

80 = 80

 

5(15) + 7(10) = 145

75 + 70 = 145

145 = 145