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.

Look at the following drawing representing the pieces of fruit in a fruit bowl. Calculate the ratio of the number of apples (orange) to the number of pears (soft white).

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.

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 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?

To prepare a very special shade of orange, a graffiti artist mixes $1.2\text{ litres}$ of red paint with $0.8\text{ litres}$ of yellow paint.

1. a) Write the ratio of the amount of red paint to yellow paint. Express it as an irreducible fraction.
2. b) If he wants to keep the same shade but only has $0.5\text{ litres}$ of yellow paint, what amount of red paint should he use? (Use the ratio obtained in the previous part).

On a treasure island map from a film, the distance between "Pirate Harbour" and "Skull Mountain" is $15\text{ cm}$. In reality, that distance is $4.5\text{ km}$.

1. a) Calculate the ratio of the map measurement to the real-life measurement (remember to convert both to the same unit, for example, centimetres).
2. b) What is the name of this special ratio used on maps?

Cian is building a scale model of a Dublin Bus city bus. The real bus is $12\text{ m}$ long and his model is $15\text{ cm}$ long. To indicate the scale on the project's data sheet, Cian writes the following:

'The scale is $\dfrac{15}{12} = \dfrac{5}{4} = 1.25$, which means that the model is $1.25$ times bigger than the bus'.

1. a) Explain the two errors that Cian has made (one related to the units of measurement and the other to the interpretation of the resulting ratio).
2. b) Correct the approach and calculate the correct numerical scale of the model, expressing it in the usual format $1:n$.

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?

To prepare a pink paint mixture, an artist uses $3$ tins of white paint for every $2$ tins of red paint.

• Write the ratio of white paint to red paint.

• If the artist decided to use $6$ tins of red paint, how many tins of white paint should he use to keep the same shade of pink?

A street artist is creating a new color "Cyber Green" by mixing blue paint and yellow paint. In her first tin, she mixed $0.75$ litres of blue with $1.2$ litres of yellow. Running out of paint, she decides to prepare a second mixture in a larger tin using $2.5$ litres of blue. How many litres of yellow must she add so that the ratio of blue to yellow is exactly the same as in the first mixture? Express the initial ratio as a simplified fraction.

Un paquete de $500$ gramos de cereales cuesta $3.50$ €. Expresa la razón entre el precio y el peso en gramos. Después, calcula el valor decimal de esa razón para saber cuánto cuesta $1$ solo gramo de cereales.

A sweet shop offers two types of bags of gummy sweets:

• Bag A: contains $250\text{ g}$ and costs $\text{€}\ 3.50$.

• Bag B: contains $400\text{ g}$ and costs $\text{€}\ 5.20$.

1. a) Calculate the price-to-weight ratio for each bag.
2. b) Which of the two bags is cheaper value for money? Justify your answer using the values obtained.

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.

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 a secondary school's vegetable garden, the simplified ratio between the number of tomato plants and the number of lettuce plants planted is $\dfrac{3}{5}$. Furthermore, the Biology teacher tells you that the total number of plants (tomatoes plus lettuces) is greater than $30$ and less than $50$.

1. a) Exactly how many tomato plants and how many lettuce plants can there be? Write all possible pairs of solutions that meet these conditions.
2. b) Justify why it would be impossible for this garden to have a total of $35$ plants while maintaining that same ratio.