Exercises: Word problems with prices

For an Art project, Marcos needs to buy $2 \text{ m}$ and $40 \text{ cm}$ of decorative ribbon. If a metre of ribbon costs $0,50 \text{ €}$, what is the total cost of the ribbon Marcos needs?

Lucía's mother has bought a rectangular rug for her bedroom measuring $3 \text{ m}$ long and $2 \text{ m}$ wide. If the price of the rug is $15 \text{ €}$ per square metre ($m^2$), how much did the rug cost?

In a stationer's, a gram of special craft paper costs $0,02 \text{ €}$. If we buy a sheet weighing $80 \text{ dg}$, how much will we have to pay?

A delivery van can transport a maximum of $1,5 \text{ t}$ (tonnes). If the transport cost is $0,10 \text{ €}$ per kilogram of load, how much will the delivery cost if the van is filled to its maximum capacity?

Lucas needs to buy network cable to connect his computer to the router in his bedroom. At the local hardware store, the cable is sold at $0,35 \text{ €}$ per metre. Since the distance he measured is $420 \text{ cm}$, Lucas calculates the price by multiplying directly: $0,35 \cdot 420 = 147 \text{ €}$. Shocked by the result, he thinks he won't be able to afford it.

1. a) Identify the mistake Lucas made and explain why it makes no sense to multiply those two numbers directly.
2. b) Correct his approach by making the necessary conversion and calculate the actual price he will have to pay at the hardware store.

In a local deli, a cured sheep's milk cheese is priced at $19,80 \text{ €}$ per kilogram. You are about to buy a wedge that, when placed on the scale, reads exactly $350 \text{ g}$.

1. a) Before doing any written calculations, mentally round the price to the tens and the weight to a simple fraction of a kilogram to make a quick estimate of the cost. Justify the values you chose for your approximation.
2. b) Perform the appropriate unit conversion and calculate the exact price of the wedge.
3. c) Check whether your initial estimate was accurate and explain why this habit of estimating beforehand helps you detect potential billing errors in a shop.

In your local greengrocer's, a kilogram of Jerte cherries costs $5,80 €$. If you decide to buy a bag containing $750 \text{ g}$ of cherries and pay with a $10 €$ note, how much change will you receive?

You want to replace the floor in your bedroom, which is rectangular with dimensions of $4 \text{ m}$ long and $350 \text{ cm}$ wide. The price of the laminate flooring you like is $18,50 €$ per square metre. What will be the total cost of the material to cover the whole floor?

For a birthday party, you need to buy $12 \text{ L}$ of orange drink. At the supermarket you have two options:

• $1,5 \text{ L}$ bottles at $1,20 €$ each.

• Packs of 6 cans of $33 \text{ cl}$ at $3,15 €$ per pack.

Calculate how much it would cost you to buy the exact $12 \text{ L}$ using only the first option. How many packs of cans would you have to buy to have at least that amount?

A farmer wants to fence off a rectangular field for his sheep measuring $1,5 \text{ hm}$ long and $80 \text{ m}$ wide. A metre of metal fencing costs $6,40 €$. Furthermore, he must leave a gap of $30 \text{ dm}$ to install a gate he has already bought. What will be the total budget to buy the required fencing?

A tanker lorry carries $15 \text{ m}^3$ of drinking water to supply a drought-affected area.

1. a) If water is sold at $0,05 €$ per decalitre ($\text{daL}$), how much is the lorry's entire load worth?
2. b) How many $5 \text{ L}$ water containers could be filled with that entire volume?

In a DIY shop, network cable is sold at $0,85 €$ per metre. You need to buy several pieces to install internet at home: one of $1250 \text{ cm}$, another of $85 \text{ dm}$ and a final piece of $4 \text{ m}$. If the shopkeeper gives you a discount of $2,50 €$ for buying more than $20 \text{ m}$ in total, how much will you have to pay in the end?

A cooperative in Jaén packages extra virgin olive oil in two different containers:

• A $5 \text{ L}$ jug for $42,50 \text{ €}$.

• A $750 \text{ mL}$ bottle for $6,90 \text{ €}$.

To find out which of the two options is cheaper per unit of volume, two classmates suggest two approaches:

• Method A (Elena): Convert the $750 \text{ mL}$ to litres and calculate the price per litre ($€/\text{L}$) of each container by dividing the cost by the capacity.

• Method B (Marta): Calculate the price per $100 \text{ mL}$ for both sizes to work with integer quantities and compare them.

1. a) Apply both methods step by step and check whether they both lead to the same decision about which container is better to buy.
2. b) Justify which method is more advantageous if a third product labelled at $1,80 \text{ €}$ per decilitre ($\text{dL}$) comes into play.

A sports centre in Cáceres has replaced the floor of its weight room, which is rectangular and measures $20 \text{ m}$ long. The total amount on the renovation invoice was $10\,800 \text{ €}$. The installation company charges a rate of $0,36 \text{ €}$ for each square decimetre ($\text{dm}^2$) of flooring laid.

1. a) Write a symbolic expression (a monomial) to calculate the total cost in euros ($C$) in terms of the installed area in square decimetres ($S$).
2. b) Using the monomial and the known total cost, deduce the total area of the weight room in $\text{dm}^2$ and convert it to square metres ($\text{m}^2$).
3. c) Find the width of the sports room and express the final result in decametres ($\text{dam}$).

An organic farmer has a citrus orchard covering an area of $0,85 \, ha$. To keep the trees hydrated during the summer, he uses an irrigation system that consumes exactly $12 \, L$ of water per square metre per day. If the price of irrigation water is $0,35 \, €$ per cubic metre ($m^3$), how much will the water bill come to after a month of $30$ days?

A cosmetics company manufactures a luxury perfume. To fill each $75 \, ml$ bottle, they use an essence with a density of $0,85 \, g/cm^3$. The production cost of the essence is $145 \, €$ per kilogram. In addition, the glass bottle costs $2,15 \, €$ and the packaging $0,80 \, €$. If they want to make a profit of $15 \, €$ per bottle sold, what should the retail price of a single bottle be?

We want to paint the four walls and ceiling of an exhibition hall shaped like a cuboid. The dimensions of the floor plan are $12 \, m$ long by $80 \, dm$ wide, and the height of the room is $350 \, cm$. We know that:

• One of the long walls has a window wall that occupies $15 \, m^2$.

• The coverage of the paint is $1 \, L$ per $10 \, m^2$.

• The paint is sold in tins of $5 \, L$ at a price of $42,50 \, €$ per tin.

Calculate the total cost of the required paint, taking into account that only full tins can be bought.

In a supermarket, we find two offers for jars of jam of the same brand:

• Option A: A $450 \, g$ jar costing $2,85 \, €$.

• Option B: A $0,6 \, kg$ jar with an offer of "$20 \, \%$ extra free" (that is, the jar contains $20 \, \%$ more mass, but the price is that of the standard $600 \, g$ jar), for a price of $3,90 \, €$.

Determine which of the two options is cheaper by calculating the price per kilogram of each one.

A cube-shaped tank with an edge of $1,5 \, m$ is full of olive oil. We know that the density of the oil is $0,92 \, kg/dm^3$. If the oil is packaged into $75 \, cl$ bottles and each bottle is sold on the international market at a price of $12,50$ dollars, what is the total value of the tank in dollars? (Assume that the tank is completely emptied).

Artificial turf is to be installed on a training pitch that measures $0,4 \, hm$ long and $250 \, dm$ wide. There are two quotes:

• Company "VerdeTotal": $18,50 \, €$ per square metre, but they charge a fixed installation fee of $450 \, €$.

• Company "PraderaPlus": $0,0022 \, €$ per square centimetre, with installation included in the price.

Which company is cheaper for this pitch, and how much money is saved compared to the other option?

An irrigation community in south-eastern Spain applies a tiered tariff for irrigation water in the summer:

• Tier 1 (up to $500 \text{ m}^3$): $0,25 \text{ €}$ per cubic metre.

• Tier 2 (volume exceeding $500 \text{ m}^3$): $0,60 \text{ €}$ per cubic metre.

A citrus farm with an area of $1,2 \text{ ha}$ consumed an average of $65 \text{ L}$ of water per square metre during the month of July.

1. a) Convert the farm's area to square metres ($\text{m}^2$) and find the total volume consumed in July expressed in cubic metres ($\text{m}^3$) and in kilolitres ($\text{kL}$).
2. b) Model the calculation of the total cost by breaking down the amounts for each tier and determine the final value of July's bill.
3. c) For August, the farmer sets a budget limit of $185 \text{ €}$. Deduce the maximum number of litres per square metre ($\text{L/m}^2$) he can use to irrigate his farm during August and interpret whether this measure requires significant water savings compared to July's consumption.

An HVAC company in Zaragoza provides a quote to install insulation on a building's roof. The cost is broken down into:

• Mineral wool: $4,50 \text{ €}$ per square metre ($\text{m}^2$).

• Waterproof membrane: $0,08 \text{ €}$ per square decimetre ($\text{dm}^2$).

• Labour: a fixed cost of $150 \text{ €}$ for travel and basic assembly, plus $2,50 \text{ €}$ per square metre installed.

1. a) Convert the price of the membrane to euros per square metre ($€/\text{m}^2$) and write a monomial that represents the combined cost of the materials in terms of the area $S$ (in $\text{m}^2$).
2. b) Write the algebraic expression for the total cost of the project $C(S)$ for an area of $S \text{ m}^2$. Explain with reasons whether this full expression is a monomial or not, based on the mathematical definition of a monomial.
3. c) The community of property owners has a roof of $0,025 \text{ hm}^2$ and has an alternative flat-rate offer of $3\,800 \text{ €}$ all-inclusive. Use your expression to decide which of the two options is more economical and quantify the savings.