In a store, pencils have one price and pens have another. 3 Pencils and 2 pens cost 78 cents. 2 pencils and 3 pens cost 72 cents. How much does 1 pencil and 1 pen cost?

Question

In a store, pencils have one price and pens have another. 3 Pencils and 2 pens cost 78 cents. 2 pencils and 3 pens cost 72 cents. How much does 1 pencil and 1 pen cost?

Help! I don't get this.

Answer 1

maybe twelve

Answer 2

It is actually a question i need to answer.

Answer 3

let x = cost of one pencil

let y = cost of one pen

3x + 2y = 78
2 x + 3y = 72

Multiply first equation by 2
and second equation by 3

2(3x + 2y) = 156
3(2x + 3y) = 216

then subtract one of the new equations from the other new equation. This will enable you to solve for y. etc.....

Answer 4

I have no idea

Answer 5

To solve this problem, let's assign variables to represent the prices of pencils and pens.

Let's say the price of one pencil is "p" (in cents) and the price of one pen is "q" (in cents).

Using the given information, we can write two equations:

Equation 1: 3p + 2q = 78 (since 3 pencils and 2 pens cost 78 cents)
Equation 2: 2p + 3q = 72 (since 2 pencils and 3 pens cost 72 cents)

To find the cost of one pencil and one pen (p + q), we need to solve the system of equations by elimination or substitution.

Let's use the elimination method:

Multiply Equation 1 by 2:
6p + 4q = 156

Multiply Equation 2 by 3:
6p + 9q = 216

Now, subtract Equation 1 from Equation 2:
6p + 9q - (6p + 4q) = 216 - 156
6p + 9q - 6p - 4q = 60
5q = 60

Divide both sides by 5:
q = 12

Now, substitute the value of q = 12 into either Equation 1 or Equation 2:
2p + 3(12) = 72
2p + 36 = 72
2p = 72 - 36
2p = 36

Divide both sides by 2:
p = 18

Therefore, one pencil costs 18 cents and one pen costs 12 cents.

So, the cost of 1 pencil and 1 pen is:
1 pencil (18 cents) + 1 pen (12 cents) = 30 cents.

Hence, 1 pencil and 1 pen cost 30 cents.