Problems with prices
A metre of ribbon costs $0,50\ €$. A kilo of cherries costs $5,80\ €$. A square metre of wooden flooring costs $18\ €$. When you know the price of one unit, you can work out the price of any amount... as long as you first convert it to that unit.
The price per unit
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…
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?
The key step: convert before multiplying
Almost all the mistakes in these problems come from multiplying without first converting the amount to the same unit as the price.
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?
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?
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,…
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?
Prices with lengths and areas
The same method works when the price is per metre or per square metre: you convert the amount to that unit and multiply.
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…
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?
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 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?
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 $6,40 €$.…
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?
Prices with capacities and comparing offers
Sometimes you have to decide which offer is better value: to compare them, work out the price of the same amount in both.
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…
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?
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…
For a birthday party, you need to buy $12 \text{ L}$ of orange drink. At the supermarket you have two options:
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$1,5 \text{ L}$ bottles at $1,20 €$ each.
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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?
Problems with several sections
Some problems mix pieces in different units: convert them all before adding and multiplying by the price.
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…
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?
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…
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?