Exercises: Word problems with equations

In the Science lab we have a balance in equilibrium, as the figure shows. On the left pan there are $2$ identical boxes (each weighing $x$ kg) and a $1$ kg weight. On the right pan there is a $7$ kg weight. Write the equation that represents this equilibrium and calculate how much each box weighs.

Marcos is playing a video game and has scored twice as many points in the current level as in the previous level. If he scores a total of $150$ points across both levels, how many points did he get in each level? Let $x$ be the points in the first level.

We are designing an esports team logo shaped like an isosceles triangle. We want the perimetre to be $30$ cm. If the base measures $10$ cm and the other two sides are equal, how long must each of those sides ($x$) be?

If you add a consecutive number (the number that comes right after) to a number, the result is $43$. Set up an equation to find out what the number is.

Amina is $3$ years older than her younger brother. If their combined age is $19$ years, how old is each of them? Let $x$ be the age of the younger brother.

A group of friends buys a family-sized pizza that costs $720$ pesos. If they have $480$ pesos left over after paying for it from the money they had collected, how much money did they have at the start? Represent the initial amount with the letter $x$.

We want to fence off a small rectangular vegetable patch to plant tomatoes. The length of the patch is twice its width. If we have used $18$ meters of fencing to completely surround it (perimeter), what are the width and length of the patch?

On a shelf in a comic book shop, there are three times as many action manga as mystery manga. If there are $48$ comics in total between both genres, how many are there of each type? Let $x$ be the mystery comics.

Three friends are comparing how many songs they have in their favorite playlist. Lucía has twice as many songs as Marcos, and Sara has 15 more songs than Marcos. If all three have a total of 155 songs altogether, how many songs does each person have in their playlist? Set up an equation where $x$ is the number of Marcos's songs.

At Adrián's birthday party, two types of invitations were handed out: digital and paper. The number of digital invitations was three times the number of paper ones. If a total of 48 invitations were sent out, how many people received a paper invitation and how many a digital one?

Marta bought a video game on offer and a new controller. The controller cost her $1\,500$ pesos less than the video game. If she paid a total of $5\,340$ pesos for both items, what is the original price of each item without counting other discounts?

In a shopping center parking lot there is a total of $32$ vehicles, including cars and motorcycles. If we count all their wheels (excluding spare tires), we get a total of $94$ wheels. Calculate how many cars and how many motorcycles are in the parking lot.

(Hint: If we let $x$ be the number of cars, the number of motorcycles will be $32 - x$).

The PE teacher has bought three boxes of tennis balls. The second box contains twice as many balls as the first, and the third box has $10$ more balls than the second. If there are $85$ balls in total, how many balls are in each box?

Héctor is 5 years older than his sister Ainhoa. In 8 years' time, the sum of their ages will be 41 years. How old is each of them now?

(Remember to add 8 years to each person's age to set up the future sum).

To balance a scale in the Science lab, we have placed a stone of unknown weight $x$ and a $12$-gram weight on the left pan. On the right pan, to keep it balanced, we had to put four equal weights, each with the same weight $x$ as the original stone. How much does the stone weigh?

On a scientific expedition through the Amazon, the team consumes $\frac{1}{4}$ of their water supply on the first day. On the second day, they consume $\frac{2}{5}$ of what was left in the tank. If after these two days they still have $135$ liters, how many liters of water did they have at the start of the expedition?

The perimeter of an isosceles triangle-shaped technology park is $110$ meters. We know that each of the equal sides measures $10$ meters more than twice the base. Calculate the length of each of the three sides of the park by setting up an equation.

In a games shop, they sold three times as many copies of an adventure game as a sports game. Furthermore, they sold $15$ fewer units of a platform game than the adventure game. If they sold a total of $125$ video games across the three titles, how many copies were sold of each one?

A digital content creator reviewed their monthly statistics. The comedy video has twice as many views as the technology video, and the travel video has $4000$ more views than the comedy video. If all three videos total $24000$ views altogether, how many views does each video have?

Salma's mother is currently three times her age. In $12$ years, her mother's age will be only twice Salma's age. How old is each of them currently? Use a table to organise the data for the present and the future.

In a piggy bank, there are $0.50$ pesos and $1$ peso coins. In total, there are $35$ coins with a total value of $26$ pesos. How many coins of each type are in the piggy bank? (Hint: if you let $x$ be the number of $1$ peso coins, the number of $0.50$ pesos coins will be $35 - x$).

Three siblings, Alberto, Berta and Carlos, want to buy a present for their parents that costs $105$ pesos. Alberto contributes an amount of money, Berta gives twice as much as Alberto, and Carlos gives $15$ pesos less than Berta. How much money does each person contribute so that they have exactly enough for the gift?