Math CentralQuandaries & Queries


Question from sandhiya, a student:

one group of people purchased 10 hotdogs and 5 soft drinks at a cost of $12.50.asecond group bought 7 hotdogs and 4 soft drinks at a cost of $9.00 find the cost of a single hot and a single soft drink.(using the row echelon form to solve)

Hi Sandhiya,

I can help get you started.

First I am going to write the cost on cents rather than dollars so that I can work with integers. Let h be the cost of a hotdog in cents and s be the cost of a soft drink in cents. Then for the first group

10 h + 5 s = 1250

and for the second group

7 h + 4 s = 900.

The augmented matrix for this system of linear equations is then

matrix 1

The first thing I notice is that the first row has a common factor of 5 so multiply the first row by 1/5

matrix 2

Multiply the first row by -3 add add it to the second row

matrix 3

Can you complete the problem now?


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