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svetlana [45]
3 years ago
6

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

Mathematics
1 answer:
Flauer [41]3 years ago
3 0
-----------------------------------------------------------------------------------------
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

----------------------------------------------------------------------------------------
Answer: The bag cost $250 and the pen cost $50
----------------------------------------------------------------------------------------
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