SAT · SAT Maths
Problem-Solving and Data Analysis
Ratios, rates, proportions, and units 7 questions
QUESTION 1 [2 marks]
Easy
A recipe requires 2 cups of flour for every 3 cups of sugar. How many cups of flour are needed for 12 cups of sugar?
Show Solution
Set up a proportion: $\dfrac{2}{3}=\dfrac{x}{12}$. Cross-multiplying: $3x=24$, so $x=8$ cups of flour.
QUESTION 2 [2 marks]
Easy
A car travels 150 miles in 3 hours at a constant speed. How far will it travel in 5 hours at the same speed?
Show Solution
Speed $=\dfrac{150}{3}=50$ miles per hour. In 5 hours: $50\times5=250$ miles.
QUESTION 3 [3 marks]
Medium
A printer produces 45 pages in 3 minutes at a constant rate. How many pages does it print in 8 minutes?
Show Solution
Rate $=\dfrac{45}{3}=15$ pages per minute. In 8 minutes: $15\times8=120$ pages.
QUESTION 4 [3 marks]
Medium
Given that 1 inch $=2.54$ cm, a board is 40 inches long. What is its length in centimeters, to the nearest tenth?
Show Solution
$40\times2.54=101.6$ cm.
QUESTION 5 [4 marks]
Hard
The quantities $x$ and $y$ vary directly. When $x=8$, $y=20$. What is the value of $y$ when $x=14$?
Show Solution
Direct variation means $y=kx$ for a constant $k$. From $x=8,\ y=20$: $k=\dfrac{20}{8}=2.5$. When $x=14$: $y=2.5\times14=35$.
QUESTION 6 [5 marks]
Hard
A recipe that serves 8 people requires $2\tfrac{1}{2}$ cups of rice. If the recipe is scaled to serve 20 people, how many cups of rice are needed?
Show Solution
Set up a proportion: $\dfrac{2.5}{8}=\dfrac{x}{20}$. Cross-multiplying: $8x=2.5\times20=50$, so $x=6.25$ cups. (Equivalently, the recipe scales by a factor of $\tfrac{20}{8}=2.5$, and $2.5\times2.5=6.25$.)
QUESTION 7 [5 marks]
Hard
Machine A can complete a job in 6 hours, and Machine B can complete the same job in 4 hours. Working together at their individual constant rates, how many hours will it take them to complete the job?
Show Solution
Machine A's rate is $\dfrac{1}{6}$ job per hour and Machine B's rate is $\dfrac{1}{4}$ job per hour. Working together, their combined rate is $\dfrac{1}{6}+\dfrac{1}{4}=\dfrac{2}{12}+\dfrac{3}{12}=\dfrac{5}{12}$ job per hour. Time to complete 1 job $=\dfrac{1}{5/12}=\dfrac{12}{5}=2.4$ hours.