Ratio and proportion

In a Year 7 class, there are $12$ pupils who play basketball and $18$ pupils who play football. Write the ratio of the number of basketball players to football players. Explain in your own words what the result means after simplifying the fraction.

In an adventure video game, your character has obtained $24$ health potions after opening $6$ magic chests. Calculate the ratio of the number of potions to the number of chests. On average, how many health potions are there in each chest?

A radio-controlled car travels a distance of $45$ metres in $15$ seconds. Calculate the ratio of distance to time. What physical quantity does this result represent?

In a basketball training session, Lucía scored $18$ three-pointers out of $30$ shots taken, while her teammate Marcos scored $14$ three-pointers out of $20$ shots.

1. a) Express the success ratio of each player as a decimal number.
2. b) Which of the two has a better success ratio? Justify your answer by comparing both values.

In your Year 7 class there are $32$ pupils in total. It is known that for every $3$ pupils who prefer PE classes, there are $5$ pupils who prefer Art.

1. a) Write the ratio of those who prefer PE to those who prefer Art.
2. b) If these are the only two options and everyone has chosen one, how many pupils prefer each subject? (Hint: notice that the sum of the terms in the simplified ratio is $3 + 5 = 8$).

In competitive video gaming, server performance is measured by the ratio of connected players to bandwidth consumed (in Mbps). The "BattleArena" server has $120$ players and consumes $450$ Mbps. On the other hand, the "GalaxyQuest" server has $85$ players and consumes $320$ Mbps. Calculate the consumption ratio per player for both servers and determine which of the two is more efficient (the one consuming fewer Mbps per player). Express the ratios as decimals.

Look at these two mixtures of water and strawberry syrup. Mixture $A$ has $2$ glasses of syrup for every $5$ glasses of water. Mixture $B$ has $4$ glasses of syrup for every $10$ glasses of water.

• Write the ratio for each mixture.

• Are these mixtures proportional? That is, will they taste the same?

In a strategy video game, to craft a "Super Speed" potion, the alchemist uses $150\text{ mg}$ of stardust for every $250\text{ ml}$ of magic water.

1. a) Express the ratio of stardust to magic water. Simplify the result and interpret what this value means.
2. b) Calculate the inverse ratio (magic water to stardust) and explain what information it gives us.