Question

A group of five golfers paid $245 to play a round of golf of the golfers, one is a member of the club and four are nonmembers. Another group of golfers consists
of four members and two nonmembers. They paid a total of $210. What is the cost for a member to play a round of golf, and what is the cost for a nonmember?

Answer 1

Answer:

M = member of the club

N = non member of the club

For the first senario:

1M + 5N = $245

Second senario:

4M + 2N = $210

We want to be able to set these two equations to eachother so let's each equation so each equations is N = something.

1M + 5N  = 245 Divide both sides by M

5N = 245/M  Divide both sides by 5

N = (245/M) / 5 = 49/(M/5)

4M + 2N = 210 Divide both sides by 4M

2N = 210/4M Divide both sides by 2

N = (210/4M) /2 = 105/2M

Our two equations are now

N =  49/(M/5) and N = 105/2M

We know N = N so ,

49/(M/5) = 105/2M  now we only have one variable so let's solve for M

$\frac{49}{M/5} = \frac{105}{2M}$  

Lets mutiply both sides by $\frac{1}{49}$ to get 49 out of the numberator on the left side

M/5 = (105/2M) * 1/49

M/5 = $\frac{\frac{15}{7} }{\frac{2}{49M} }$  multiply both sides by 5

M = (75/7) / (10/49M) mutiply both sides by 10/49M

10/49 M = 75/7  divide by 10/49

M = 105/2 = 52.5

So a paid membership is $52.50. We can solve for an unpaid membership by plugging in $52.50 for M in either of our orginal equations.

First Senario: 1M + 5N = $245

52.50 + 5N = 245 subtract both sides by 52.50

5N = 192.5 divide both sides by 5

N = 38.5

So an non-member costs $38.5. We can check our answers by solving for the second senario usinmg the values we found for M and N.

4M + 2N = $210

4(52.5) + 2 (38.5) = 287 so I messed up somewhere

Step-by-step explanation: