Six pencils and three rubbers cost #1170. Five pencils and two rubbers cost#920. How much does each cost?

1 answer

Let's denote the cost of one pencil as \( p \) and the cost of one rubber as \( r \).

From the given information, we can set up the following system of equations based on the costs:

  1. \( 6p + 3r = 1170 \) (Equation 1)
  2. \( 5p + 2r = 920 \) (Equation 2)

We can solve this system of equations step-by-step.

First, we can simplify Equation 1 by dividing everything by 3:

\[ 2p + r = 390 \quad \text{(Equation 3)} \]

Next, we can multiply Equation 3 by 2 to align the coefficient of \( r \):

\[ 4p + 2r = 780 \quad \text{(Equation 4)} \]

Now, we will subtract Equation 2 from Equation 4:

\[ (4p + 2r) - (5p + 2r) = 780 - 920 \]

This simplifies to:

\[ -1p = -140 \]

So, we find:

\[ p = 140 \]

Now that we have \( p \), we can substitute it back into Equation 3 to find \( r \):

\[ 2(140) + r = 390 \]

This simplifies to:

\[ 280 + r = 390 \]

Then, solving for \( r \):

\[ r = 390 - 280 = 110 \]

Thus, the costs are:

  • The cost of one pencil \( p \) is #140.
  • The cost of one rubber \( r \) is #110.

Final answer: Pencil = #140, Rubber = #110.