SAT Question 67c0200a: Percentages answer and explanation with Desmos solution

54$.I{t}^{\prime }sgiventhatthenumber$a$is$70 %$lessthanthepositivenumber$b$.Therefore,$a = \left( 1 - \frac{70}{100} \right) b$,whichisequivalentto$a = \left( 1 - 0.70 \right) b$,or$a = 0.30 b$.I{t}^{\prime }salsogiventhatthenumber$c$is$80 %$greaterthan$a$.Therefore,$c = \left( 1 + \frac{80}{100} \right) a$,whichisequivalentto$c = \left( 1 + 0.80 \right) a$,or$c = 1.80 a$.Since$a = 0.30 b$,substituting＄0.30b$ for $a$ in the equation $c=1.80a$ yields $c=1.80\left(0.30b\right)$, or $c=0.54b$. Thus, $c$ is $0.54$ times $b$. Note that 27/50, .54, .540, and 0.54 are examples of ways to enter a correct answer.