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 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: \( #110 \)