Question

A local sorority sold hot dogs and bratwursts at the spring fling picnics. The first day they sold 8 dozen hot dogs and 13 dozen bratwursts for $316.20.The second day they sold 10 dozen hot dogs and 15 dozen bratwursts for a total of $375.00. How much did each​ cost? Solve this system using an inverse matrix.​ (Hint: It's easier to leave the dozens in the problem until the last​ step.)

Answer 1

Answer: Cost of each hot dog and bratwursts would be $1.1 and $1.35 each.

Step-by-step explanation:

Since we have given that

Cost of each dozen hot dogs be 'x'.

Cost of each dozen bratwursts be 'y'.

The first day they sold 8 dozen hot dogs and 13 dozen bratwursts for $316.20.

So, the equation would be

$8x+13y=\ 316.20$

.The second day they sold 10 dozen hot dogs and 15 dozen bratwursts for a total of $375.00.

So, the equation would be

$10x+15y=\ 375.00\\\\2x+3y=\ 75$

So, the equations becomes

$8x+13y=316.20--------------(2)\\\\(2x+3y=75)\times 4\\\\\implies 8x+12y=300------------(1)$

So, by elimination method, we get that

$8x+13y=316.20\\\\(-)8x+(-)12y=(-)300\\\\--------------\\y=\ 16.20$

Put the value of y in the eq(1), we get that

$2x+3y=75\\\\2x+3(16.20)=75\\\\2x+48.6=75\\\\2x=75-48.60\\\\2x=26.4\\\\x=\dfrac{26.4}{2}\\\\x=\ 13.2$

Hence, the cost of hot dogs would be $\dfrac{13.2}{12}=\ 1.1$

And the cost of bratwursts would be $\dfrac{16.2}{12}=\ 1.35$