Respuesta :
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.
SOLVING
[tex]\Large\maltese\underline{\textsf{A. What is Asked}}[/tex]
Find two consecutive even numbers whose sum is 126.
[tex]\Large\maltese\underline{\textsf{B. This problem has been solved!}}[/tex]
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.
[tex]\bf{x+x+2=126}[/tex] | arrange the like terms
[tex]\bf{2x+2=126}[/tex] | subtract 2
[tex]\bf{2x=124}[/tex] | 2 was subtracted from BOTH sides
[tex]\bf{x=62}[/tex]
[tex]\cline{1-2}[/tex]
Now, the second integer is [tex]\bf{x+2}[/tex].
[tex]\bf{So\;let's\;put\;the\;first\;number\;into\;the\;formula\;x+2}[/tex].
[tex]\bf{62+2}[/tex] | add (mental arithmetic)
[tex]\bf{64}[/tex]
[tex]\cline{1-2}[/tex]
[tex]\bf{Result:}[/tex]
[tex]\bf{=Number\;1=62}\\\\=Number\;2=64[/tex]
[tex]\LARGE\boxed{\bf{aesthetic \not1 \theta l}}[/tex]
