Felicity has 30pottery pieces for sale in her store. Each vase, v, sells for $21and each bowl, b, sells for $12.50. If Felicity sells all of her inventory, she will make $477. This situation can be represented by the system of equations shown below.(1 point)Felicity's store has______vases and_____bowls for sale

Answer 1

To determine the number of vases (v) and bowls (b) Felicity has for sale, we start by setting up a system of equations based on the problem statement.

1. The first equation comes from the total number of pottery pieces: \[ v + b = 30 \]

2. The second equation comes from the total sales amount: \[ 21v + 12.5b = 477 \]

Now, we can solve this system of equations step by step.

From the first equation, we can express \( b \) in terms of \( v \): \[ b = 30 - v \]

Next, we substitute this expression for \( b \) into the second equation: \[ 21v + 12.5(30 - v) = 477 \]

Expanding this equation: \[ 21v + 375 - 12.5v = 477 \]

Combining like terms: \[ (21 - 12.5)v + 375 = 477 \] \[ 8.5v + 375 = 477 \]

Now, we isolate \( v \) by subtracting 375 from both sides: \[ 8.5v = 477 - 375 \] \[ 8.5v = 102 \]

Next, solve for \( v \): \[ v = \frac{102}{8.5} = 12 \]

Now that we have \( v \), we can find \( b \): \[ b = 30 - v = 30 - 12 = 18 \]

Therefore, Felicity's store has 12 vases and 18 bowls for sale.

In summary: Felicity's store has 12 vases and 18 bowls for sale.