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F. Incorrect. Since you are given that the ratio of the integers is $5\text{:}3\text{:}2$, try writing the 3 integers in terms of a variable, $x$: $n_1=5x$, $n_2=3x$, and $n_3=2x$. Because the sum of these 3 integers is 180, set up an equation to solve for x and use that value to calculate the smallest integer. You might have solved for x and stopped.

G. Correct. Since you are given that the ratio of the integers is $5\text{:}3\text{:}2$, write the 3 integers in terms of a variable, $x$: $n_1=5x$, $n_2=3x$, and $n_3=2x$. Because the sum of these 3 integers is 180, set up the equation $5x+3x+2x=180$. Then, solve the equation for x, resulting in $x=18$. Finally, substitute $18$ for x to calculate the smallest integer: $n_3=2x=2\left(18\right)=36$.

H. Incorrect. Since you are given that the ratio of the integers is $5\text{:}3\text{:}2$, try writing the 3 integers in terms of a variable, $x$: $n_1=5x$, $n_2=3x$, and $n_3=2x$. Because the sum of these 3 integers is 180, set up an equation to solve for x and use that value to calculate the smallest integer. You might have solved for x but then calculated $n_2$ instead of $n_3$: $n_2=3\left(18\right)=54$.

J. Incorrect. Since you are given that the ratio of the integers is $5\text{:}3\text{:}2$, try writing the 3 integers in terms of a variable, $x$: $n_1=5x$, $n_2=3x$, and $n_3=2x$. Because the sum of these 3 integers is 180, set up an equation to solve for x and use that value to calculate the smallest integer. You may have solved for x but then calculated $n_1$ instead of $n_3$: $n_1=5\left(18\right)=90$.