SUED SEE SAMPLE PROBLEM A painter mixes red paint with yellow paint to make orange paint. The painter has a total of 10 liters of paint.The red paint costs 5 per liter, and the yellow paint costs 4 per liter. If the total cost of the paint mixture is 47 how many liters of red paint and how many liters of yellow paint were used? Amount of paint: __ .......... Answer: __ .. litters of red paint and. __ __

To solve this problem, we need to set up a system of linear equations based on the given information.<br /><br />Let's define the variables:<br />- Let x be the amount of red paint (in liters)<br />- Let y be the amount of yellow paint (in liters)<br /><br />We are given the following information:<br />1. The total amount of paint is 10 liters.<br />2. The cost of red paint is $5 per liter.<br />3. The cost of yellow paint is $4 per liter.<br />4. The total cost of the paint mixture is $47.<br /><br />We can set up the following system of linear equations:<br /><br />Equation 1: x + y = 10 (The total amount of paint is 10 liters)<br />Equation 2: 5x + 4y = 47 (The total cost of the paint mixture is $47)<br /><br />Now, we can solve this system of equations to find the values of x and y.<br /><br />Step 1: Solve Equation 1 for y:<br />y = 10 - x<br /><br />Step 2: Substitute the expression for y into Equation 2:<br />5x + 4(10 - x) = 47<br />5x + 40 - 4x = 47<br />x = 7<br /><br />Step 3: Substitute the value of x into Equation 1 to find y:<br />7 + y = 10<br />y = 3<br /><br />Therefore, the painter used 7 liters of red paint and 3 liters of yellow paint.