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

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

Now, we can solve these equations simultaneously.

First, let's simplify Equation 1. We can divide the entire equation by 3:

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

Next, we can use Equation 3 to express \( r \) in terms of \( p \):

\[
r = 390 - 2p
\]

Now we'll substitute this expression for \( r \) back into Equation 2:

\[
5p + 2(390 - 2p) = 920
\]

Expanding this gives:

\[
5p + 780 - 4p = 920
\]

Now, combine like terms:

\[
p + 780 = 920
\]

Subtract 780 from both sides:

\[
p = 140
\]

Now we know the cost of one pencil is \( p = 140 \). Next, we'll substitute \( p \) back into Equation 3 to find \( r \):

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

This simplifies to:

\[
280 + r = 390
\]

Subtract 280 from both sides:

\[
r = 110
\]

Hence, the costs are:

- Cost of one pencil: \( \#140 \)
- Cost of one rubber: \( \#110 \)