Math Gold Medalist

Lor

2022 AMC 8 

Problem 13

How many positive integers can fill the blank in the sentence below?

“One positive integer is _____ more than twice another, and the sum of the two numbers is $28$.”

$\textbf{(A) } 6 \qquad \textbf{(B) } 7 \qquad \textbf{(C) } 8 \qquad \textbf{(D) } 9 \qquad \textbf{(E) } 10$

Translating Word Problems Into Equations

If the blank is d then a=2b+d and a+b=28

Then 3b+d=28 and b can be from 1 to 9

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   Solution