Problem
3. A shop sales almond and jellybeans. A customer buys $3 \mathrm{lb}$ of almond and $8 \mathrm{lb}$ of jellybeans with a cost of $\$ 23.00$. Another day, he buys $5 \mathrm{lb}$. of almond and $2 \mathrm{lb}$. of jellybeans with a cost of $\$ 10.00$. Assuming the costs remain the same, determine the cost of each $\mathrm{lb}$. of almond and each $\mathrm{lb}$. of jellybeans.
Solution
Step 1 ：Let the cost of 1 lb of almond be \(a\) and the cost of 1 lb of jellybeans be \(j\)
Step 2 ：Set up the equations based on the given information: \(3a + 8j = 23\) and \(5a + 2j = 10\)
Step 3 ：Solve the system of equations to find the values of \(a\) and \(j\)
Step 4 ：The cost of each \( \mathrm{lb} \) of almond is \(\boxed{\$1.00}\) and the cost of each \( \mathrm{lb} \) of jellybeans is \(\boxed{\$2.50}\)
