Solving systems by substitution word problem

Question

If i can be shown how to do it step by step that would be nice too

 

1. The price of admission to an amusement park is $45 for adults and $15 for children. A group of six people [A+C=6] visit the park and pay a total of $150 [45A+15C=150]. If you solve the system of equations, which equation can be used to find how many adults attended?

 

A. 45(6-C)+15C=150

B.45A+15(6-A)=150

C.A=C-6

D.C=A-6

Answer 1

Hi Nicholas,

 

For this problem they have given you the two equations to use:

 

A+C = 6      means 6 people, some adults some children, went to the park

 

45A + 15C = 150  this equation puts the money on each variable.  Price per adult, price per child, total cost.

 

To find how many adults attended, we need to solve for A, not C.

 

Answer choices C and D do not work because if you solve the equation A+C=6 for A, you would get A=6-C (that is different from A=C-6).  The same thing happens if you solve for C.  You get C=6-A.

 

Answer choice A only has the variable C in it.  So, if we solve for C, we would have the number of children who attended. 

 

Answer choice B is correct because we can solve for A in this equation to get the number of adults.

 

To solve the system:

Take first equation and solve it for C.  You will get C=6-A.

Substitute 6-A in for C in the second equation.

45A+15(6-A)=150

Solve the equation for A.

45A + 90-15A = 150

30A + 90 = 150

30A = 60

A=2

Therefore, 2 adults attended.

PS if you wanted to find the number of children, just substitute 2 in for A in the original equation and solve for C.

2+C=6

C=4