Given:
Sum = 102
What is asked:
Largest number
Mathematical sentence:
[tex]x + y + z = 102[/tex]
Let:
x = first number
y = x + 1 = 2nd number
z = x + 2 = 3rd number
Solution:
[tex]x + y + z = 102 \\ x + (x + 1) + (x + 2) = 102 \\ 3x + 3 = 102 \\ 3x = 102 - 3 \\ \frac{3x}{3} = \frac{99}{3} \\ x = 33[/tex]
The first number is 33.
Solve for the other two numbers using the value of x.
[tex]y = x + 1 \\ y= 33 + 1 \\ y = 34[/tex]
The second number is 34.
[tex]z = x + 2 \\ z = 33 + 2 \\ z= 35[/tex]
The third number is 35.
Check:
[tex]x + y + z = 102 \\ 33 + 34 + 35 = 102 \\ 102 = 102[/tex]
The three numbers are 33, 34, and 35.
The largest number is 35.
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