To find the cost of a pen and the cost of a pencil, we can set up a system of linear equations based on the information given. Let's denote:
- The cost of a pencil as [tex]\( a \)[/tex]
- The cost of a pen as [tex]\( b \)[/tex]
We are given two conditions:
1. The cost of 3 pencils and 4 pens is K1.04.
2. The cost of 3 pencils and 2 pens is 64 toea. Note that 64 toea is equal to K0.64 (since 100 toea = 1 kina).
We can set up the following equations based on these conditions:
[tex]\[
3a + 4b = 1.04 \quad \text{(Equation 1)}
\][/tex]
[tex]\[
3a + 2b = 0.64 \quad \text{(Equation 2)}
\][/tex]
To find the values of [tex]\( a \)[/tex] and [tex]\( b \)[/tex], we will solve these two equations simultaneously.
Step-by-Step Solution:
1. Write the system of equations:
[tex]\[
3a + 4b = 1.04
\][/tex]
[tex]\[
3a + 2b = 0.64
\][/tex]
2. Subtract Equation 2 from Equation 1 to eliminate [tex]\( a \)[/tex]:
[tex]\[
(3a + 4b) - (3a + 2b) = 1.04 - 0.64
\][/tex]
This simplifies to:
[tex]\[
2b = 0.40
\][/tex]
3. Solve for [tex]\( b \)[/tex]:
[tex]\[
b = \frac{0.40}{2}
\][/tex]
[tex]\[
b = 0.20
\][/tex]
So, the cost of a pen, [tex]\( b \)[/tex], is K0.20.
4. Substitute [tex]\( b \)[/tex] back into Equation 2 to solve for [tex]\( a \)[/tex]:
[tex]\[
3a + 2(0.20) = 0.64
\][/tex]
[tex]\[
3a + 0.40 = 0.64
\][/tex]
Subtract 0.40 from both sides:
[tex]\[
3a = 0.64 - 0.40
\][/tex]
[tex]\[
3a = 0.24
\][/tex]
5. Solve for [tex]\( a \)[/tex]:
[tex]\[
a = \frac{0.24}{3}
\][/tex]
[tex]\[
a = 0.08
\][/tex]
So, the cost of a pencil, [tex]\( a \)[/tex], is K0.08.
Summary:
- The cost of a pencil is K0.08.
- The cost of a pen is K0.20.
