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3 years ago

Solve a Mixture Word Problem

Mathematics

2 answers:

saw5 [17]3 years ago

6 0

Answer: Orlando mixed five pounds of cereal squares and 25 pounds of nuts.

stich3 [128]3 years ago

3 0

Answer:

5 lbs cereal squares.

25 Ibs nuts.

Step-by-step explanation:

Let x be the weight of nuts in pounds and y be the weight of cereal squares in pounds.

Total weight of the party mix is 30 pounds.

$x+y=30$ ..... (1)

It is given that,

Cost of nuts = $7 per pound

Cost of cereal = $4 per pound

The cost of mix = $6.50 per pound.

$7x+4y=6.50\times 30$

$7x+4y=195$ ..... (2)

Substitute the value of x in equation (2) from equation (1).

$7(30-y)+4y=195$

$210-7y+4y=195$

$-3y=195-210$

$-3y=-15$

Divide both sides by -3.

$y=5$

Substitute y=5 in equation (1).

$x+5=30$

Subtract both sides by 5.

$x=30-5$

$x=25$

Therefore, he use 25 lbs of nuts and 5 lbs cereal squares for party mix.

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Step-by-step explanation:

$\underline{ \underline{ \text{Given}}} :$

$\tt{ {A}^{T} = \begin{bmatrix} 2 & - 4 \\ 4 & 3 \\ \end{bmatrix}}$

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The new matrix obtained from a given matrix by interchanging it's rows and columns is called the transposition of matrix. It is denoted by $\sf{ {A}^{T}}$ . Again , Interchange it's rows and columns in order to find ' A '.

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$\tt{ {A}^{2} - 5A+ 22I}$

Here, I refers to identity matrix. A diagonal matrix in which all the elements of leading diagonal are 1 ( unit ) is called unit or identity matrix.

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⟼ $\begin{bmatrix} 2 \times 2 + 4 \times ( - 4)& 2 \times 4 + 4 \times 3 \\ - 4 \times 2 + 3 \times ( - 4) & - 4 \times 4 + 3 \times 3 \\ \end{bmatrix} - \begin{bmatrix} 10 & 20 \\ - 20& 15 \\ \end{bmatrix} + \begin{bmatrix} 22 & 0 \\ 0 & 22 \\ \end{bmatrix}$

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⟼ $\begin{bmatrix} - 12 & 20\\ - 20& - 7 \\ \end{bmatrix} - \begin{bmatrix} 10 & 20 \\ - 20 & 15 \\ \end{bmatrix} + \begin{bmatrix} 22 & 0 \\ 0 & 22 \\ \end{bmatrix}$