Question

The sum of two numbers is 38. The greater number is 8 more than the other number. Find each number. Use a system of linear equations to justify your answer

Answer 1

Call x and y the 2 numbers.

x + y = 32

x - y = 8

2x = 40 -> x = 20, and y = 32 - 20 = 12.

Answer 2

The two numbers whose sum is 38 are 15 and 23, while the linear equation that will describe the system is 2x+8=38.

What are the two numbers?

As it is given to us, the sum of two numbers is 38. The greater number is 8 more than the other number.

As we know that the greater number is 8 more than the other number, therefore, the first number be x. therefore, the other number is (x+8).

The sum of the two numbers is 38.

$x+ (x+8) = 38\\\\2x+8=38\\\\2x= 38-8\\\\2x= 30\\\\x= 15$

Substitute the value of x,

so the other number is (x+8)=23.

Thus, the two numbers whose sum is 38 are 15 and 23.

Use a system of linear equations to justify your answer.

As we know that according to the system of linear equations the system can be given to us,

$x+(x+8) = 38\\\\x+ x + 8 = 38\\\\2x+ 8 = 38$

Hence, the system can be given by the equation 2x+8=38.

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