Review: Ratio, Multiway Ratio, Proportions, Conversions, & Speed

In a classroom, the ratio of books to students is 2 to 5. The ratio of math books to the total number of books is 3 to 8. If there are 270 math books, how many students are there?

Mathematical Equivalence

ON

Sarah owns twice as many blue shoes as green shoes, three times as many yellow shoes as blue shoes, and half as many pink shoes as green shoes. What is the ratio of the number of pink shoes to the number of yellow shoes she owns?

Three colleagues, Dana, Evan, and Fiona, invested money into a startup. Dana contributed $40, Evan contributed $30, and Fiona contributed $50. After a year, the startup made a profit of $3,000. They decide to split this profit in the same ratio as their initial investment. How much money will Evan receive?

• $600

• $750

• $500

• $550

A banner designed by Leo is 4 feet wide and 3 feet tall. For an event, it needs to be enlarged to 12 feet wide. How tall will the banner be when it is enlarged proportionally?
The banner will be ​ (a)   tall.

• 9 feet
• 8.5 feet
• 10 feet

Eighteen friends gathered for a pizza party, where they ordered enough pizzas for 27 people, given the portions. If they wanted to order just enough pizza for everyone with no leftovers, how many friends' portions should each pizza account for?

Each pizza should account for ​ (a)   friends' portions.

• 1.5
• 2
• 3

There are approximately 454 grams in a pound. A recipe calls for a half-pound of chicken. How many grams of chicken are needed? Round your answer to the nearest whole number.

Mathematical Equivalence

ON

10,000 square meters is 1 hectare, and 2.47 acres is one hectare. Then 1 acre is equal to ... square meters

Mathematical Equivalence

ON

I usually bike to work, which takes me 20 minutes. Today, I had to stop for 5 minutes due to a flat tire, reducing my biking speed by half for the remainder of the trip. If my usual speed is twice as fast as my speed with the flat tire, how many minutes in total did it take me to get to work today?

• 35 minutes

• 3/4 hours

• 40 minutes

• 1/2 hours

Two dogs run around a circular track 300 feet long in the same direction. One dog runs at a steady rate of 15 feet per second, the other at a steady rate of 12 feet per second. Suppose they start at the same point and time. What is the least number of seconds that will elapse before they are again together?

Mathematical Equivalence

ON

Boston is 295 miles from New York City along a certain route. A car starts from Boston at 1:00 PM and travels along the route toward New York at a steady rate of 50 mph. Another car starts from New York at 1:30 PM and travels along this route toward Boston at a steady rate of 40 mph. At what time do the cars pass each other?
Format answer: Example 1:45