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3 years ago

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sports warehouse had a sale on two models of baseball gloves. Model A sold for $30.00, and model B sold for $45.25. A total of 5

2 gloves were sold. The total amount of sales earned on the gloves, excluding tax, was $2,078.50. How many model B baseball gloves were sold

1 answer:

alexandr402 [8]3 years ago

6 0

Answer:

18 model A gloves and 34 model B gloves

Step-by-step explanation:

Set up 2 equations based on the given information

Let 'x' represent the number of Model A gloves sold

Let 'y' represent the number of Model B gloves sold

Then..

$30x + $45.25y = $2,078.50 represents the total sold in dollars

x + y = 52 represents the total number of gloves sold

Solve the second equation for either variable...

x = 52 - y

Now plug this into the first equation...

$30(52 - y) + $45.25y = $2,078.50 {x became 52 - y}

Now solve for y...

$1,560 - $30y + $45.25y = $2,078.50

$15.25y = $518.50 (combine y terms, subtract $1,560 from both sides)

y = 34 (divide both sided by $15.25, dollar signs cancel out)

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Factor each expression 36abc +54ad

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Answer:

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Step-by-step explanation:

36abc + 54ad

Step 1: Find the Highest Common Factor of each

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Step 2: Factor out with HCF

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3 years ago

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Answer:

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Step-by-step explanation:

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2 years ago

Marni has 11 ounces of walnuts. She needs 6 ounces for one recipe and pound for another. There are 16 ounces in 1 pound.

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2 years ago

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Formulate the situation as a system of two linear equations in two variables. Be sure to state clearly the meaning of your x- an

slega [8]

Answer:

1) There were 33 $4,000 investors and 27 $8,000 investors.

2) The solution in x = 4, y = 9.

3) There were 24 nickels and 56 dimes.

Step-by-step explanation:

1) A lawyer has found 60 investors for a limited partnership to purchase an inner-city apartment building, with each contributing either $4,000 or $8,000. If the partnership raised $348,000, then how many investors contributed $4,000 and how many contributed $8,000?

I am going to say that:

x is the number of investors that contributed 4,000.

y is the number of investors that contributed 8,000.

Building the system:

There are 60 investors. So:

$x + y = 60$

In all, the partnership raised $348,000. So:

$4000x + 8000y = 348000$

I am going to simplify by 4000. So:

$x + 2y = 87$

Solving the system:

The elimination method is a method in which we can transform the system such that one variable can be canceled by addition. So:

$1)x + y = 60$

$2)x + 2y = 87$

I am going to multiply 1) by -1. So we have

$1)-x - y = -60$

$2)x + 2y = 87$

By addition, the x are going to cancel each other

$-x + x - y + 2y = -60 + 87$

$y = 27$

For x:

$x + y = 60$

$x = 60-y = 60-27 = 33$

There were 33 $4,000 investors and 27 $8,000 investors.

2) Solve the system by row-reducing the corresponding augmented matrix.

$2x + y = 17$

$x + y = 13$

This system has the following augmented matrix:

$\left[\begin{array}{ccc}2&1&17\\1&1&13\end{array}\right]$

To help the row reducing, i am going to swap the first with the second line:

$L1 L2$

So we have:

$\left[\begin{array}{ccc}1&1&13\\2&1&17\end{array}\right]$

Now, reducing the first column.

$L2 = L2 - 2L1$

So we have:

$\left[\begin{array}{ccc}1&1&13\\0&-1&-9\end{array}\right]$

Now we do:

$L2 = -L2$

And the matrix is:

$\left[\begin{array}{ccc}1&1&13\\0&1&9\end{array}\right]$

Now to reduce the second column, we do:

$L1 = L1 - L2$

$\left[\begin{array}{ccc}1&0&4\\0&1&9\end{array}\right]$ .

So the solution is:

x = 4, y = 9.

3) A jar contains 80 nickels and dimes worth $6.80. How many of each kind of coin are in the jar?

I am going to say that x is the number of nickels and y is the number of dimes.

Each nickel is worth 5 cents and each dime is worth 10 cents.

Building the system:

There are 80 coins in all:

$x + y = 80$

They are worth $6.80. So:

$0.05x + 0.10y = 6.80$

Solving the system:

$1)x + y = 80$

$2)0.05x + 0.10y = 6.80$

I am going to divide 1) by -10, so we can cancel y. So:

$1)-0.10x - 0.10y = -8$

$2)0.05x + 0.10y = 6.80$

Adding:

$-0.10x + 0.05x - 0.10y + 0.10y = -8 + 6.80$

$-0.05x = -1.2$ *(-100)

$5x = 120$

$x = \frac{120}{5}$

$x = 24$

Also

$x + y = 80$

$y = 80-x = 80-24 = 56$

There were 24 nickels and 56 dimes.

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3 years ago

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Sunny_sXe [5.5K]

Answer:

24/25

Step-by-step explanation:

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2 years ago

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