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joja [24]
3 years ago
13

A delivery truck is transporting boxes of two size: the combined weight of a large box and a small box is 65 pounds. The truck i

s transporting 60 large boxes and 55 small boxes if the truck is carrying a total of 3775 pounds in boxes, how much does each type of box weigh?
Mathematics
1 answer:
Bas_tet [7]3 years ago
6 0

pretty much about the same as before.

a = weight of a large box

b = weight of a small box.

we know their combined weight is 65 lbs, thus a + b = 65.

we also know that the truck has 60 large ones, and 55 small ones, thus 60*a is the total weight for the large ones and 55*b is the total weight for the small ones, and we know that is a total of 3775, 60a + 55b = 3775.

\bf \begin{cases} a+b=65\\ \boxed{b}=65-a\\ \cline{1-1} 60a+55b=3775 \end{cases}\qquad \qquad \stackrel{\textit{substituting on the 2nd equation}}{60a+55\left( \boxed{65-a} \right)=3775} \\\\\\ 60a+3575-55a=3775\implies 5a+3575=3775\implies 5a=200 \\\\\\ a=\cfrac{200}{5}\implies \blacktriangleright a = 40 \blacktriangleleft \\\\\\ \stackrel{\textit{since we know that}}{b=65-a\implies }b=65-40\implies \blacktriangleright b=25\blacktriangleleft

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ANSWER

The correct answer is m=45,n=12.

<u>EXPLANATION</u>

We were given the matrix equation;

\left[\begin{array}{cc}n-1&6\\-19&m+3\end{array}\right] +\left[\begin{array}{cc}-1&0\\16&-8\end{array}\right] =\left[\begin{array}{cc}10&6\\-3&40\end{array}\right].


We must first simplify the Left Hand Side of the equation by adding corresponding entries.


\left[\begin{array}{cc}n-1+-1&6+0\\-19+16&m+3-8\end{array}\right]=\left[\begin{array}{cc}10&6\\-3&40\end{array}\right].


That is;


\left[\begin{array}{cc}n-2&6\\-3&m-5\end{array}\right]=\left[\begin{array}{cc}10&6\\-3&40\end{array}\right].

Since the two matrices are equal, their corresponding entries are also equal. we equate corresponding entries and solve for m and n.


This implies that;


n-2=10


We got this equation from row one-column one entry of both matrices.


n=12


Also, the row three-column three entries of both matrices will give us the equation;


m-5=40


m=45


Hence the correct answer is m=45,n=12.


The correct option is option 2






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B)√5 < 2.4<√62.24 < 2.4 < 2.45 True

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Please help me ASAP! I need this done rn :(((( thank you ! :)
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Explanation:

1 gallon = 8 pints

2 gallons = 8 pints + 8 pints = 16 pints

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Number of pints         Number of gallons

             8                                     1

            16                                     2

            24                                    3

Ratio of pints to gallons = 8 : 1

<u>Convert pints to gallons:</u>

From the table,

8 pints = 1 gallon

1 pint = \frac{1}{8} gallon

<u>Equation:</u>

From the table, 8p = g

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