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

$\bf{x=62}$

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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)

$\bf{64}$

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$\bf{Result:}$

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

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Answer 2

Answer:

62 and 64

Step-by-step 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.