Word Problem

Question

The school that Jacob goes to is selling tickets to a spring musical On the first day of ticket sales the school sold 9 senior citizen tickets and 8 child tickets for a total of $138. The school took in #124 on the second day by selling 10 senior citizen tickets and 4 child tickets. Find the price of a senior citizen ticket and the price of a child ticket.

 

a. senior-$10 child-$6

b. senior- $6 Child- $8

c. senior- $7 Child- $10

d. Senior $7 Child $4

Answer 1

We use s to represent the cost of a senior's ticket and c to represent the cost of a child's ticket. Thus, our system of equations, from the two sentences is:

9s+8c=138

10s+4c=124

To solve this system of equations, we can use a variety of techniques; in this case I will use a linear combination of the two equations to eliminate one variable. First, multiply the second equation by -2.

9s+8c=138
-20s-8c=-248

Then, add the two equations to eliminate c.

-11s = -110

Divide both sides by -11.

s=10

Thus the cost of a senior's ticket is $10. The only choice is (a). But we want to be sure...

Return to either of the original equations in our original system to determine c.

9(10)+8c=138

Subtract 90 (or 9*10) from both sides.

8c=48

Divide by 8.

c=6

Check against other original equation.

10(10)+4(6) =?= 124

124 =√= 124

Yay!

 

It should be mentioned that you could have also just checked each of the answer choices against the original equations.

10(10)+4(6) =?= 124   yep

10(6)+4(8) =?= 124     nope

10(7)+4(10) =?= 124   nope

10(7)+4(4) =?= 124    nope

 

Answer 2

The answer is A.

Let S= Price of senior ticket

Let C = Price of a child ticket.

 

This leads us to the following two equations based on sales

1. 9 * S + 8 * C = 138

2.  10 * S + 4 * C = 124

 

Let's use equation 1 to express S in terms of C

subtract 8*C from both sides

9*S = 138 - 8*C

 

Let's use equation 2 to express C as a function of S:

Subtract 10*S from both sides

4*C = 124 - 10*S

Divide both sides by 4

C = 31 - (10/4)*S

 

The value C  in equation 1 can now be replaced with an expression which only contains S as an unknown, thus simplifying it to an equation of 1 unknown variable

9*S = 138 - 8*(31-(10/4)*S)

9*S = 138 -248 + (80/4)*S

9*S = 138  -248 + 20*S

-Subtract 20*S from both sides

-11*S = 138-248

-11*S = -110

11*S = 110

S = 10

 

We now know the excact value of S and can replace it with that value in any equation. Let's do that to our simplified equation 2:

C = 31 - (10/4)*10

C = 31 - 100/4

C = 31 - 25

C = 6

 

We can test this answer by plugging 10,6 into the original equations and testing the equality:

9*10 + 8*6 = 138

90 + 48 = 138

138 = 138  check

 

10*10 + 4*6 = 124

100 + 24 = 124

124 = 124 check