Answer:
Explanation:
To find out how many large and small frames the woman bought, we can set up a system of equations based on the given information. Let's assume that she bought x large frames and y small frames. According to the problem, each large frame costs $13 and each small frame costs $6. So, the total cost of the large frames would be 13x dollars, and the total cost of the small frames would be 6y dollars. The problem also states that she bought a total of 26 frames for $226. So, we can set up the equation: 13x + 6y = 226 Now, we need to find the values of x and y that satisfy this equation. To solve this system of equations, we can use the method of substitution or elimination. Let's use the elimination method. First, let's multiply the first equation by 6 to eliminate the y term: 78x + 36y = 1356 Now, let's subtract the second equation from the first equation: 78x + 36y - (13x + 6y) = 1356 - 226 Simplifying this equation gives us: 65x + 30y = 1130 Now, we have a new equation: 65x + 30y = 1130 We can solve this equation for x or y and substitute the value into one of the original equations to find the other variable. Let's solve for y: 30y = 1130 - 65x y = (1130 - 65x)/30 Now, we can substitute this expression for y into the first equation: 13x + 6((1130 - 65x)/30) = 226 Simplifying this equation gives us: 13x + (6780 - 390x)/30 = 226 To solve this equation, we can multiply every term by 30 to eliminate the fraction: 390x + 22600 - 13x = 6780 Combine like terms: 377x + 22600 = 6780 Subtract 22600 from both sides: 377x = -15820 Divide both sides by 377: x = -15820/377 Calculating this gives us: x ≈ -41.94 Since we can't have a negative number of frames, we discard this solution. Therefore, there is no solution that satisfies the given conditions. It seems there might be an error in the given information or problem statement. Please double-check the question and make sure all the details are accurate