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3 years ago

Multi step equations

Mathematics

1 answer:

baherus [9]3 years ago

3 0

Answer:

what is the problem?

Step-by-step explanation:

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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

kicyunya [14]

Answer:

1 hot dog costs $0.75

1 bratwurst costs $1.35

Step-by-step explanation:

Let x and y be the price per dozen of hot dogs and bratwursts respectively.

The first day they sold 8 dozen hot dogs and 13 dozen bratwursts for $282.60

8x + 13y = 282.60

The second day they sold 10 dozen hot dogs and 15 dozen bratwursts for a total of $333.00

10x + 15y = 333

and we have the linear system

which can be written in matrix form as

$\bf \left(\begin{array}{cc}8&13\\10&15\end{array}\right)\left(\begin{array}{c}x\\ y\end{array}\right)=\left(\begin{array}{c}282.60\\333\end{array}\right)$

The solution would be given by

$\bf \left(\begin{array}{c}x\\ y\end{array}\right)=\left(\begin{array}{cc}8&13\\10&15\end{array}\right)^{-1}\left(\begin{array}{c}282.60\\333\end{array}\right)$

We have

$\bf \left(\begin{array}{cc}8&13\\10&15\end{array}\right)^{-1}=\left(\begin{array}{cc}-3/2&13/10\\1&-4/5\end{array}\right)$

hence

$\bf \left(\begin{array}{c}x\\ y\end{array}\right)=\left(\begin{array}{cc}-3/2&13/10\\1&-4/5\end{array}\right)\left(\begin{array}{c}282.60\\333\end{array}\right)=\left(\begin{array}{c}9\\ 16.2\end{array}\right)$

Now,

if a dozen hot dogs cost $9, 1 hot dog costs 9/12 = $0.75

if a dozen bratwursts cost $16.2, 1 bratwurst costs 16.2/12 = $1.35

4 0

3 years ago

A recipe uses 114 cups of sugar for a batch of brownies. Tommy makes 10 batches of cookies for a bake sale. How many cups of sug

Nastasia [14]

He needs 1140 cups of sugar. (total # of cups of sugar) = 114c

8 0

3 years ago

Read 2 more answers

If john makes a contribution to a charity fund at school, the average contribution size will increase by 50% reaching $75 per pe

Sonja [21]

Answer:

$Z= 75*6 -250=200$

So then the correct answer is B. $200.

Step-by-step explanation:

Notation

Let X be the average contribution size before John makes his contribution.

Let Y be the total contribution size before John makes his contribution.

Let Z be John's contribution.

We know that for this case $ 75 represent the original average amount before the contribution with 50% increase so we can set up the following equation in order to find the original average amount

$1.5 X = 75$