Question

Find two consecutive even numbers
whose sum is 126.

Answer 1

SOLVING

`\Large\maltese\underline{\textsf{A. What is Asked}}`

Find two consecutive even numbers whose sum is 126.

`\Large\maltese\underline{\textsf{B. This problem has been solved!}}`

For now, let the first number be x.

Let the second number be x+2. (consecutive even numbers are right next to each other, like 2 and 4)

These two integers add up to 126. This gives us an equation that we can solve in terms of x.

`\bf{x+x+2=126}` | arrange the like terms

`\bf{2x+2=126}` | subtract 2

`\bf{2x=124}` | 2 was subtracted from BOTH sides

`\bf{x=62}`

`\cline{1-2}`

Now, the second integer is
`\bf{x+2}`.

`\bf{So\;let's\;put\;the\;first\;number\;into\;the\;formula\;x+2}`.

`\bf{62+2}` | add (mental arithmetic)

`\bf{64}`

`\cline{1-2}`

`\bf{Result:}`

`\bf{=Number\;1=62}\\\\=Number\;2=64`

`\LARGE\boxed{\bf{aesthetic \\ot1 \theta l}}`

Answer 2

62 and 64

Explanation:

Let x be the first number

Let y be the 2nd number

Given,

x + 2 = y (Consecutive even numbers)

x - y = -2 (rearranged) - Equation 1

x + y = 126 - Equation 2

Now we can solve for x and y to find the 2 numbers by using substitution method in solving simultaneous equations.

x = y-2 (rearranged equation 1)

Now we substitute equation 1 into equation 2.

y - 2 + y = 126

2y - 2 = 126

2y = 126 + 2

2y = 128

y = 128 / 2

= 64

Now we will substitute y into equation 1.

x - 64 = -2

x = -2 + 64

= 62

Therefore the 2 numbers are 62 and 64.