Question

The larger of two numbers is 2 more than 4 times the smaller. Their sum is 67. Find the numbers. Let x represent the larger number and y represent the smaller number.

Answer 1

To find the two numbers, first, set up equations based on the given conditions and then solve the system of equations. The smaller number is found to be 13 and the larger number is 54.

Step-by-step explanation:

The problem you are trying to solve is a system of linear equations where the larger number x is 2 more than 4 times the smaller number y, and their sum is 67. To find the numbers, let's set up the equations based on the given information:

• Equation 1 (larger number in terms of smaller number): x = 4y + 2
• Equation 2 (sum of the numbers): x + y = 67

We can substitute the expression from Equation 1 into Equation 2 to find the value of y:

• Substitute x: (4y + 2) + y = 67
• Combine like terms: 5y + 2 = 67
• Solve for y: 5y = 65
• Divide by 5: y = 13

Now that we have the value of y, we can find the value of x by plugging it back into Equation 1:

• x = 4(13) + 2
• x = 52 + 2
• x = 54

So the smaller number is 13 and the larger number is 54.