In a stationery store, pencils have one price and pens have another price. Two pencils and three pens cost $0.78. But three pencils and two pens cost $0.72. How much does one pencil cost?

To find the cost of one pencil, we can set up a system of equations based on the given information. Let's denote the cost of one pencil as "x" and the cost of one pen as "y". Step 1: Set up the equations: From the given information, we can set up two equations: Equation 1: 2x + 3y = 0.78 (Two pencils and three pens cost $0.78) Equation 2: 3x + 2y = 0.72 (Three pencils and two pens cost $0.72) Step 2: Solve the system of equations: To solve the system of equations, we can use the method of substitution or elimination. Let's use the method of elimination. Multiply Equation 1 by 3 and Equation 2 by 2 to eliminate the "y" variable: Equation 1: 6x + 9y = 2.34 Equation 2: 6x + 4y = 1.44 Subtract Equation 2 from Equation 1: (6x + 9y) - (6x + 4y) = 2.34 - 1.44 6x - 6x + 9y - 4y = 0.9 5y = 0.9 Step 3: Solve for "y": Divide both sides of the equation by 5: 5y/5 = 0.9/5 y = 0.18 Step 4: Substitute the value of "y" back into one of the original equations to solve for "x": Using Equation 1: 2x + 3(0.18) = 0.78 2x + 0.54 = 0.78 2x = 0.78 - 0.54 2x = 0.24 Divide both sides of the equation by 2: 2x/2 = 0.24/2 x = 0.12 Therefore, one pencil costs $0.12.