Question

3 7 pens and 53pencils together cost 820 while 53 pens and 37 pencils together cost 980. Find the cost of a pen and a pencil

Answer 1

$\textbf {Hey there, here is the solution.}$

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STEP 1: Define x and y

Let the cost of pen be x and the cost of pencil be y

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STEP 2: Form equations:

37 pens and 53 pencils cost 820

⇒ 37x + 53y = 820

53 pens and 37 pencils cost 980

⇒ 53x + 37y = 980

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STEP 3: Solve x and y:

37x + 53y = 820 ------------- [ 1 ]

53x + 37y = 980 ------------- [ 2 ]

.

[ 1 ] x 53 = 1961x + 2809y = 43460 ------------- [ 3 ]

[ 2] x 37 = 1961x + 1369y = 36260 ------------- [ 4 ]

.

[ 3 ] - [ 4 ] :

1440y = 7200

y = 5 ------------- Substitute into [ 1 ]

37x + 53y = 820

37x + 53(5)y = 820

37x + 265 = 820

37x = 555

x = 15

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STEP 4: Find the price of pen and pencil:

Pen = x = 15

Pencil = y = 5

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Answer: Each pen costs 15 and each pencil costs 5

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⭐$\textbf {Cheers}$⭐

Answer 2

Step-by-step explanation:

STEP 1: Define x and y

Let the cost of pen be x and the cost of pencil be y

.

STEP 2: Form equations:

37 pens and 53 pencils cost 820

⇒ 37x + 53y = 820

53 pens and 37 pencils cost 980

⇒ 53x + 37y = 980

.

STEP 3: Solve x and y:

37x + 53y = 820 ------------- [ 1 ]

53x + 37y = 980 ------------- [ 2 ]

.

[ 1 ] x 53 = 1961x + 2809y = 43460 ------------- [ 3 ]

[ 2] x 37 = 1961x + 1369y = 36260 ------------- [ 4 ]

.

[ 3 ] - [ 4 ] :

1440y = 7200

y = 5 ------------- Substitute into [ 1 ]

37x + 53y = 820

37x + 53(5)y = 820

37x + 265 = 820

37x = 555

x = 15

.

STEP 4: Find the price of pen and pencil:

Pen = x = 15

Pencil = y = 5

.

Answer: Each pen costs 15 and each pencil costs 5

.