Question

The sum of two numbers is 634. The second number is 58 more than twice the first number. Find both numbers.

In the space below, you need to:
a. Define your variables.
b. Write two linear equations . Explain the meaning of your solution in a complete sentence

Answer 1

The first number is 192 and the second number is 382.

Step-by-step explanation:

To solve this problem, we can define the variables:

Let x = the first number

Let y = the second number

Based on the information given, we can write two linear equations:

x + y = 634 (equation 1)

y = 2x + 58 (equation 2)

To solve the equations, we can use the method of substitution or elimination. Let's use the substitution method:

Substitute equation 2 into equation 1:

x + (2x + 58) = 634

Simplify:

3x + 58 = 634

Subtract 58 from both sides:

3x = 576

Divide by 3:

x = 192

Substitute x = 192 into equation 2:

y = 2(192) + 58

y = 382

Therefore, the first number is 192 and the second number is 382.