Question

A graphic design firm placed two orders for computers from Apple Inc. For their web design department, they purchased 2MacBook Pro notebooks and 4iMac desktops for a total order price of $14,794. For their graphic arts department they purchased 3MacBook Pro notebooksand 5 iMac desktops for a total order price of $19,892. Assume the prices of the computers did not change between orders.a.Create a system of equations to model this situation. Be sure to state what your variables represent.[2pts] b.Algebraically solve the equationsyou created in part a. Interpretyour final answer using a complete sentence and appropriate units. (You will not receive full credit if a trial and error method is used in place of an algebraic method.)

Answer 1

(a) System of equations are

$2x+4y=14794\\3x+5y=19892$

(b) The cost of MacBook is $2,799

The cost of iMac is $2,299

Given :

Firm purchased 2MacBook Pro notebooks and 4iMac desktops for a total order price of $14,794

they purchased 3MacBook Pro notebooks and 5 iMac desktops for a total order price of $19,892.

Let x be the cost of MacBook Pro

and y be the cost of iMac

Now frame the equation using given information

2 MacBook +4 iMac= 14794

2x+4y=14794

3 MacBook +5 iMac= 19892

3x+5y=19892

System of equations are

$2x+4y=14794\\3x+5y=19892$

To solve for x  and y , Lets solve the second equation for x

$3x+5y=19892\\3x=19892-5y\\x=\frac{19892-5y}{3}$

Substitute x in first equation and solve for y

$2\cdot \frac{19892-5y}{3}+4y=14794\\\frac{39784+2y}{3}=14794\\\frac{3\left(39784+2y\right)}{3}=14794\cdot \:3\\39784+2y=44382\\2y=4598\\y=2299$

Substitute y value in the x equation

$\mathrm{\:}x=\frac{19892-5y}{3}\\x=\frac{19892-5\cdot \:2299}{3}\\x=2799$

The cost of MacBook is $2,799

The cost of iMac is $2,299

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