1. Stating the problem: We are given three equations involving division and variables $x$ and $y$: $$1.350 \div 90 = 540$$ $$1.125 \div x = 450$$ $$450 \div 30 \div y$$ We need to find the values of $x$ and $y$. 2. Analyze the first equation: $$1.350 \div 90 = 540$$ This seems incorrect because $1.350 \div 90$ is not equal to 540. Let's check the calculation: $$1.350 \div 90 = \frac{1.350}{90} = 0.015$$ So the first equation might be a hint or a misprint. Let's focus on the second and third equations. 3. Solve the second equation for $x$: $$1.125 \div x = 450$$ Rewrite as: $$\frac{1.125}{x} = 450$$ Multiply both sides by $x$: $$1.125 = 450x$$ Divide both sides by 450: $$x = \frac{1.125}{450}$$ Show cancellation: $$x = \frac{\cancel{1.125}}{\cancel{450}} = 0.0025$$ But this value does not match any options. Let's check if the decimal points are misplaced. Possibly the numbers are in thousands, so $1.125$ means $1125$ and $1.350$ means $1350$. Recalculate with $1125$: $$1125 \div x = 450 \Rightarrow x = \frac{1125}{450} = 2.5$$ Still no match. Let's check the third expression: $$450 \div 30 \div y$$ This equals: $$\frac{450}{30 \times y} = \frac{15}{y}$$ We want to find $y$ such that this expression equals a certain value. 4. Check the options for $x$ and $y$: Options: a. $x=57$, $y=160$ b. $x=315$, $y=315$ c. $x=75$, $y=180$ d. $x=75$, $y=150$ e. $x=705$, $y=1155$ 5. Test option c (since $x=75$ is common): Check second equation: $$1125 \div 75 = 15$$ But the equation says $1125 \div x = 450$, so 15 is not 450. Try option d: $$1125 \div 75 = 15$$ Again 15, not 450. Try option b: $$1125 \div 315 \approx 3.571$$ No. Try option a: $$1125 \div 57 \approx 19.74$$ No. Try option e: $$1125 \div 705 \approx 1.595$$ No. 6. Since none matches, let's try the original numbers as given: $$1.125 \div x = 450 \Rightarrow x = \frac{1.125}{450} = 0.0025$$ Similarly, for the third expression: $$450 \div 30 \div y = ?$$ Calculate $450 \div 30 = 15$, so: $$15 \div y = ?$$ We want to find $y$ such that $15 \div y$ equals one of the options' $y$ values. Try option c: $y=180$ $$15 \div 180 = 0.0833$$ No. Try option d: $y=150$ $$15 \div 150 = 0.1$$ No. Try option a: $y=160$ $$15 \div 160 = 0.09375$$ No. Try option b: $y=315$ $$15 \div 315 = 0.0476$$ No. Try option e: $y=1155$ $$15 \div 1155 = 0.01299$$ No. 7. Since the problem is ambiguous, the best match is option d with $x=75$ and $y=150$ because $75$ appears twice and $150$ is a reasonable value. Final answer: $$x = 75, \quad y = 150$$