Question

SET UP BUT DO NOT SOLVE the following system of linear equations:

A company sells three sizes of fruit trays. The small size contains 200 gr of watermelons and 100 gr of grapes. The medium size contains 400 gr of watermelons, 100 gr of pineapples, and 300 gr of grapes. The large size contains 600 gr of watermelons, 200 gr of pineapples, and 400 gr of grapes. Suppose that the company receives an order for 28 kg of watermelons, 6 kg of pineapples, and 19 kg of grapes. How many of each size tray does the company need to fill this order exactly?

Answer 1

A company sells 3 sizes of fruit trays.

One tray of the small size contains 200 gms of watermelons, and 100 gms of grapes.

One tray of the medium size contains 400 gms of watermelons, 100 gms of pineapples, and 300 gms of grapes.

One tray of the large size contains 600 gms of watermelons, 200 gms of pineapples, and 400 gms of grapes.

Now, the company receives an order for 28 kg of watermelons, 6 kg of pineapples, and 19 kg of grapes.

Let, x be the number of trays of the small size, y be the number of trays of the medium size, and z be the number of trays of the large size, that the company needs, to deliver this order.

Now, 200 gms mean 0.2 kg, 100 gms mean 0.1 kg; 400 gms mean 0.4 kg, 300 gms mean 0.3 kg; 600 gms mean 0.6 kg.

Now, the total watermelon must be 28 kg.

So, 0.2x+0.4y+0.6z=28

Now, the total pineapple must be 6 kg.

So, 0.1y+0.2z=6

Now, the total grapes must be 19 kg.

So, 0.1x+0.3y+0.4z=19

So, the linear system of equations, that we set up is