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Galina-37 [17]
3 years ago
12

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.)
Mathematics
1 answer:
Sergeu [11.5K]3 years ago
4 0

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

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