Question

A tent manufacturer produces two models, the Outback and the Bush Walker. From earlier sales records, it is known that 20% more of the Outback model is sold than the Bush Walker. A profit of $200 is made on each Outback sold, but $350 is made on each Bush Walker. If during the next year a profit of $177 000 is planned, how many of each model must be sold?

Answer 1

To find out how many of each model must be sold, set up a system of equations using the given information. The profit made on each model is known, and the total profit planned is given. Solve the system of equations to find the number of each model that must be sold. We get $177,000.

Step-by-step explanation:

To find out how many of each model must be sold, we can set up a system of equations using the given information.

Let's say the number of Bush Walker models sold is x.

Then the number of Outback models sold would be 20% more than x, which can be expressed as 1.2x.

The profit made on each Bush Walker model is $350, so the total profit from selling x Bush Walkers would be 350x. Similarly, the profit made on each Outback model is $200 and the total profit from selling 1.2x Outbacks would be 200(1.2x) = 240x.

We are given that the total profit planned is $177,000, so we can set up the equation 350x + 240x = 177,000.

Simplifying the equation, we get 590x = 177,000. Dividing both sides by 590, we find that x = 300.

Therefore, 300 Bush Walker models and 1.2(300) = 360 Outback models must be sold to achieve a profit of $177,000.