SAT · Math · Problem-Solving and Data Analysis
Razones, proporciones, velocidades y cambios de unidades.
3 cuadernos cuestan 7,50 $ → 1 cuaderno cuesta 2,50 $ → 8 cuadernos cuestan 20 $.
Intenta responder antes de abrir la solución. Las preguntas están en el idioma del examen.
A car travels $150$ miles in $2.5$ hours at a constant speed. What is the car's speed, in miles per hour?
Respuesta correcta: A. $60$
Speed is distance divided by time: $\frac{150}{2.5}=60$ miles per hour.
$75$ divides by $2$ instead of $2.5$. $150$ is the distance, and $375$ multiplies the distance by the time.
A car travels 180 kilometers in 2.5 hours at a constant speed. At this speed, how many kilometers does the car travel in 40 minutes?
Respuesta numérica (escribes el número).
Respuesta: 48
Speed = $180\div2.5=72$ kilometers per hour. 40 minutes is $\frac{40}{60}=\frac{2}{3}$ of an hour, so the distance is $72\times\frac{2}{3}=48$ kilometers.
In a bag of marbles, the ratio of red marbles to blue marbles is $3$ to $5$. After $12$ red marbles are added to the bag, the ratio of red marbles to blue marbles is $9$ to $10$. How many blue marbles are in the bag?
Respuesta numérica (escribes el número).
Respuesta: 40
Let the original numbers be $3k$ red and $5k$ blue. After adding $12$ red marbles, $\frac{3k+12}{5k}=\frac{9}{10}$. Cross-multiply: $30k+120=45k$, so $15k=120$ and $k=8$. There are $5\cdot 8=40$ blue marbles (and $24$ red marbles at first).
Check: $\frac{24+12}{40}=\frac{36}{40}=\frac{9}{10}$.