Exercises: Word problems with equations

In an eSports tournament, Alex's team scored three times as many points as Salma's team. If together the two teams scored a total of $152$ points, how many points did each team get?

Aisha is $4$ years older than her younger brother, Iker. In $6$ years' time, the sum of their ages will be $32$ years. Calculate the current age of each person by setting up a linear equation.

A school vegetable garden of rectangular shape needs to be fenced off to protect the crops. We know that the length of the garden is $5$ meters more than the width and that $38$ meters of fencing were needed to completely enclose it. What are the dimensions of the garden?

A group of friends buys tickets for a concert. "Standing" tickets cost $300$ pesos more than "seated" tickets. If they buy one of each type and the total bill is $1\,700$ pesos, what is the price of each ticket?

The sum of three race numbers from a race, which turn out to be three consecutive integers, is equal to $63$. What numbers are those three runners wearing on their shirts?

A food delivery driver carries twice as many pizzas as burgers in their backpack. If they are carrying $12$ orders in total between pizzas and burgers, how many of each type are there?

Lucía has started saving to buy a tablet costing $4{,}800$ pesos. She already has $1{,}200$ pesos saved and, from now on, she is going to save $240$ pesos of her allowance each week. How many weeks will it take her to have enough money for the purchase?

Calculate the side length of a square billboard, knowing that if its side length were increased by $2$ meters, its area would increase by $16$ square meters.

Find three consecutive integers such that the sum of the first two is equal to three times the third minus 14.

A new rectangular play area is being designed in a municipal park. It is known that the length of the area must be $5$ meters greater than the width. If the total area allocated for play is $150$ $m^2$, calculate the dimensions (length and width) of the area.

Currently, a father's age is three times that of his daughter. In $12$ years' time, the father's age will be only double that of his daughter. How old is each of them now?

Two cyclists, Lucía and Marcos, are at a distance of $60$ $km$ apart and decide to meet at an intermediate point. Lucía sets off from $A$ towards Marcos at a constant speed of $20$ $km/h$. At the same time, Marcos sets off from $B$ towards Lucía at a speed of $10$ $km/h$. How long will it take them to pass each other, and at what distance from point $A$ will they meet?

In a gourmet shop, two types of coffee are to be mixed. "Arabica" coffee costs $240$ pesos/kg and "Robusta" coffee costs $160$ pesos/kg. If we want to obtain a mixture of $20$ $kg$ priced at $210$ pesos/kg, how many kilograms of each type of coffee should we use?

Find a natural number such that the difference between its square and three times its value is equal to $40$. Is the solution to this problem unique in the set of natural numbers? Justify your answer by setting up the corresponding equation.

A group of friends wants to buy a birthday present that costs $2\,400$ pesos. At first there was a certain number of people, but at the last minute $2$ more friends joined, which meant each person had to pay $100$ pesos less. How many friends were originally in the group?

Calculate the dimensions of an isosceles triangle knowing that the unequal side is $4$ $cm$ less than each of the equal sides and that the total perimeter is $26$ $cm$. Once you have found the sides, calculate the area of the triangle.

A graphic designer is working on a new company logo. The design consists of a central rectangle for the name, surrounded by a decorative border of uniform thickness $x$. The inner rectangle has dimensions of $12\text{ cm}$ by $8\text{ cm}$. If the total area of the logo (including the border) must be exactly double the area of the inner rectangle, what should the thickness $x$ of the border be?

A mother's current age is the square of her daughter's age. In $9$ years' time, the mother's age will be only three times the age her daughter will be then. Find their current ages.

Two cities, $A$ and $B$, are separated by a distance of $155\text{ km}$. At 10:00 h, a cyclist departs from $A$ towards $B$ at a constant speed of $20\text{ km/h}$. An hour and a half later, a motorbike departs from $B$ towards $A$ at a speed of $80\text{ km/h}$. At what time will they pass each other, and at what distance from city $A$ will the meeting take place?

In a chemistry laboratory, $20\text{ liters}$ of an acid solution at $25\%$ concentration is needed. The technician has two containers: one with a $10\%$ acid mixture and another with a concentrated $50\%$ mixture. How many liters from each container must be mixed to obtain the desired concentration?

Mario won $\$24\,000$ in a programming competition and divided it into two parts to deposit into two different financial products. The first offers an annual return of $4\%$, while the second, which is riskier, offers $7\%$ annually. If at the end of the year the total profit obtained was $\$1\,260$, how much money did he allocate to each product?

The area of a right-angled triangle is $30\text{ cm}^2$ and its hypotenuse is $13\text{ cm}$. Calculate the lengths of the two legs of the triangle.

Two pipes connected to a tank can fill it together in $4\text{ hours}$. If used separately, the smaller diameter pipe takes $6\text{ hours}$ longer than the larger diameter pipe to fill the full tank. How long would each pipe take on its own?