Question

Best Buy advertised a 32-inch model television for $349 and a 50-inch model television for $469. During the month of October, they sold 44 of the two models for total sales of $17,516. How many of each model were sold in October?

Answer 1

By using a system of linear equations, it was determined that Best Buy sold 29 of the 32-inch model televisions and 15 of the 50-inch model televisions in October.

Step-by-step explanation:

We need to find out how many 32-inch and 50-inch televisions were sold given the total sales and amounts sold of each model. Let's define x as the number of 32-inch TVs sold for $349 each, and y as the number of 50-inch TVs sold for $469 each. The problem gives us two equations based on the information:

349x + 469y = $17,516 (total sales)

1. x + y = 44 (total televisions sold)

Now, we can use substitution or elimination to solve these equations. If we rearrange the second equation, we can express y in terms of x, which is y = 44 - x. Substituting y in the first equation:

349x + 469(44 - x) = $17,516.

Simplify and solve for x:

349x + 20636 - 469x = $17,516,

-120x = $17,516 - 20636,

x = (20636 - $17,516)/120,

x = 29. Thus, 29 of the 32-inch models were sold.

To find the number of 50-inch TVs:

y = 44 - x,

y = 44 - 29,

y = 15. Therefore, 15 of the 50-inch models were sold.