Question

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

Answer 1

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.