Question

A cup and saucer together cost 20.50. A cup and two saucers cost 27.00. Find the cost of a cup and of a saucer

Answer 1

Let the cost of a cup be \( c \) and the cost of a saucer be \( s \).

We can set up the following equations based on the information given:

1. \( c + s = 20.50 \) (Equation 1: cost of a cup and saucer)
2. \( c + 2s = 27.00 \) (Equation 2: cost of a cup and two saucers)

Now, we can solve these equations step by step.

First, we can solve Equation 1 for \( c \):

\[
c = 20.50 - s
\]

Next, we substitute \( c \) from this equation into Equation 2:

\[
(20.50 - s) + 2s = 27.00
\]

Now simplify the equation:

\[
20.50 - s + 2s = 27.00
\]
\[
20.50 + s = 27.00
\]

Now, solve for \( s \):

\[
s = 27.00 - 20.50
\]
\[
s = 6.50
\]

Now that we have the cost of a saucer, we can substitute \( s = 6.50 \) back into Equation 1 to find the cost of a cup:

\[
c + 6.50 = 20.50
\]
\[
c = 20.50 - 6.50
\]
\[
c = 14.00
\]

Thus, the cost of a cup is \( \text{14.00} \) and the cost of a saucer is \( \text{6.50} \).

**Summary:**
- Cost of a cup (\( c \)): $14.00
- Cost of a saucer (\( s \)): $6.50