Merlin wants to make more money selling fake beards this month than he did last month. All black beards in his shop cost the same amount of money, and all red beards in his shop cost

Question

\[\$25\].
Let
\[B\] represent the number of black beards and
\[R\] represent the number of red beards that Merlin can sell to make more money than he made last month.
\[20B+25R > 350\]
According to the inequality, how much money did Merlin make last month, and how much does each black beard cost?
Merlin made
\[\$\]
350
last month, and each black beard costs
\[\$\]
20
.
Can Merlin achieve his goal by selling
\[5\] black beards and
\[10\] red beards?

Answer 1

To determine if Merlin can achieve his goal of making more money by selling 5 black beards and 10 red beards, we first calculate the total revenue from these sales.

• Each black beard costs $20.
• Each red beard costs $25.

Now, calculate the total amount from selling 5 black beards and 10 red beards:

\[ \text{Total from black beards} = 5 \times 20 = 100 \text{ dollars} \] \[ \text{Total from red beards} = 10 \times 25 = 250 \text{ dollars} \]

Adding these amounts together gives:

\[ \text{Total Revenue} = 100 + 250 = 350 \text{ dollars} \]

Now, let's check whether this amount (350 dollars) meets the condition specified in the inequality:

The inequality given is:

\[ 20B + 25R > 350 \]

We substitute \(B = 5\) and \(R = 10\):

\[ 20(5) + 25(10) = 100 + 250 = 350 \]

This is not greater than 350; it equals 350.

Thus, selling 5 black beards and 10 red beards does not allow Merlin to make more money than he did last month.

In conclusion:

• Merlin made $350 last month.
• Each black beard costs $20.
• No, he cannot achieve his goal by selling 5 black beards and 10 red beards since the total is not greater than $350.