A pencil and pen cost $200. Six pencils cost the same as two pens. Find the cost of a pencils and a pen.​

x = cost of a pen, y = cost of a pencil

x + 2y = 55 and 2x + y = 50

We want to know: 3y = ?

We'll use substitution as it's the easiest for me.

If x + 2y = 55 then x = 55 - 2y (-2y each side)

We can then substitute this value for x in the other equation:

2x + y = 50 => 2(55–2y) + y = 50

Now we just need to combine like terms:

2(55 - 2y) + y = 50 Distribute 2

110 - 4y + y = 50 Combine terms -4y and y

110 - 3y = 50 Subtract 110 from both sides

-3y = -60 Multiply by -1 on both sides

3y = 60 Final answer

Three pencils cost Rs60

Note: Divide each side by 3 to derive that each pencil costs Rs20

Pencils are $20.

Pens are $60.

Step-by-step explanation:

Pencil is a. Pen is b.

b + 2a = 55

2b + a = 50

3y = ?

b + 2a = 55

b - 2a = 55 - 2a - 2a

2b + a = 50

2(55 - 2a) + a = 50

110 - 4a + a = 50

110 - 3a = 50

110 - 110 - 3a = 50 - 110

- 3a = - 60

- 3a × - 1 = - 60 × - 1

3a = 60

3a ÷ 3 = 60 ÷ 3

a = 20

6a = 2b

$120 = 2b

$120 ÷ 2 = 2b ÷ 2

$60 = b

answer: 140

step-by-step explanation:

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