Question

The sum of two numbers is 42. the larger number is 12 more than 4 times the smaller number. write a system of equations and solve the system algebraically to find the numbers

Answer 1

To solve the system of equations, set up the sum of the two numbers equal to 42. Use algebraic manipulation to find the values of the smaller and larger numbers.

Step-by-step explanation:

To solve this problem, we can set up a system of equations based on the given information:

Let x be the smaller number.

Then the larger number is 4x + 12.

The sum of the two numbers is 42, so we have the equation:

x + (4x + 12) = 42

Simplifying, we can combine like terms:

5x + 12 = 42

Subtracting 12 from both sides:

5x = 30

Finally, dividing both sides by 5:

x = 6

The smaller number is 6.

To find the larger number, we substitute the value of x back into the expression 4x + 12:

4(6) + 12 = 24 + 12 = 36

The larger number is 36.