3bags and 4 pens together cost 950 dollars whereas 4 bags and 3 pens cost 1150 dollars write two simultaneous equations

Given information

3 bags + 4 pens = $950
4 bags + 3 pens = $1150


Form the 2 equations

Let x be the cost of 1 bag.
Let y be the cos of 1 pen.

3x + 4y = 950
4x + 3y = 1150


Solve for x and y

3x + 4y = 950  (1)
4x + 3y = 1150 (2)


Equation (1) x 4

12x + 16y = 3800 (1a)


Equation (2) x 3

12x + 9y = 3450   (2a)


Equation (1a) - (2a)

 (12x + 16y) - (12x + 9y) = 3800 - 3450
7y = 350
y = 350 ÷ 7
y = 50 


Substitute y = 50 into equation (1)

3x + 4 (50)  = 950
3x + 200 = 950
3x = 950 - 200
3x = 750
x = 250


Find cost of a bag and a pen

Bag  = x = $250
Pen = y = $50


The bag cost $250 and the pen cost $50

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