Final answer:
To meet the Timber Hill Tennis Club's sales goal with the sale of 50 memberships, they would need to sell 12 tennis rackets. This is found using the linear equation 72x + 150y = 5400, representing their sales for memberships and rackets respectively.
Step-by-step explanation:
The problem involves creating a linear equation to represent the sales goal of the Timber Hill Tennis Club, which sells memberships for $72 each and tennis rackets for $150 each. Their monthly sales goal is $5400. To express this situation as a linear equation, we can let x represent the number of memberships sold and y represent the number of rackets sold. The total revenue generated from memberships is 72x, and the revenue from rackets is 150y. The linear equation taking into account both products would be given by:
72x + 150y = 5400
To graph this equation, we have the x-axis representing the number of memberships and the y-axis representing the number of rackets. When 50 memberships are sold, we replace x with 50 in our equation and solve for y to find out how many rackets need to be sold:
72(50) + 150y = 5400
3600 + 150y = 5400
Subtract 3600 from both sides:
150y = 1800
Divide both sides by 150:
y = 12
So, if the club sells 50 memberships in a month, they must sell 12 rackets to meet their goal.