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

Question

21-03-2018
Mathematics

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

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Аноним Аноним · Answer 1 · 2018-03-21T05:46:50+01:00

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

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Form the 2 equations
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Let x be the cost of 1 bag.
Let y be the cos of 1 pen.

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

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Solve for x and y
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3x + 4y = 950 -------------- (1)
4x + 3y = 1150 ------------- (2)

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Equation (1) x 4
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12x + 16y = 3800 ------------- (1a)

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Equation (2) x 3
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12x + 9y = 3450 ------------- (2a)

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Equation (1a) - (2a)
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(12x + 16y) - (12x + 9y) = 3800 - 3450
7y = 350
y = 350 ÷ 7
y = 50

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Substitute y = 50 into equation (1)
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3x + 4 (50) = 950
3x + 200 = 950
3x = 950 - 200
3x = 750
x = 250

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Find cost of a bag and a pen
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Bag = x = $250
Pen = y = $50

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