Exercises: Problems with equations

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

Marcus is playing a video game and scored twice as many points in the current level as in the previous level. If between the two levels he has a total of $150$ points, how many points did he get in each level? Call $x$ the points scored in the first level.

We are designing a logo for an esports team in the shape of an isosceles triangle. We want the perimeter to be $30$ cm. If the base measures $10$ cm and the other two sides are equal, how much must each of those sides ($x$) measure?

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

Chloe is $3$ years older than her little brother. If their ages add up to $19$ years, how old is each of them? Call $x$ the age of the little brother.

A group of friends buys a large pizza that costs $\$12$. If after paying for it they have $\$8$ left over from the money they collected, how much money did they have at the beginning? Represent the initial amount with the letter $x$.

We want to fence a small rectangular garden plot to plant tomatoes. The length of the plot is twice the width. If we used $18$ feet of fencing to completely surround it (perimeter), what are the width and length of the plot?

On a shelf in a comic book store, there are three times as many action manga as mystery ones. If there are $48$ comics in total between both genres, how many are there of each kind? Call $x$ the mystery comics.

Three friends are comparing how many songs they have on their favorite playlist. Ashley has twice as many songs as Marcus, and Sarah has 15 more songs than Marcus. If between the three of them they have a total of 155 songs, how many songs does each one have on their playlist? Set up an equation where $x$ is the number of songs Marcus has.

For Ethan's birthday, 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, how many people received the paper invitation and how many received the digital format?

We want to design a rectangular area for an esports tournament in the school gym. The length of the area must be $8$ feet greater than the width. If we need exactly $56$ feet of safety tape to enclose the total perimeter, what are the dimensions (length and width) of the gaming area?

Emma bought a video game on sale and a new controller. The controller cost her $\$25$ less than the video game. If she paid a total of $\$89$ for both items, what is the original price of each item without counting other discounts?

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

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

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

Hector is 5 years older than his sister Olivia. In 8 years, the sum of their ages will be 41 years. How old is each of them currently?

(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 placed a stone of unknown weight $x$ and a $12$ gram weight on the left pan. On the right pan, for it to be balanced, we had to put four identical 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 supplies 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 $135$ gallons, how many gallons of water did they have at the start of the expedition?

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

In a video game store, they have sold three times as many copies of "Elden Ring" as of "FIFA". In addition, they have sold $15$ fewer units of "Zelda" than of "Elden Ring". If they sold $125$ video games in total among the three titles, how many copies of each were sold?

A digital content creator reviewed his 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 the three videos have a total of $24000$ views, how many views does each video have?

Ashley's mother is currently three times as old as she is. In $12$ years, the mother will be twice as old as Ashley. How old is each of them currently? Use a table to help you organize the data for the present and the future.

In a piggy bank, there are $\$0,50$ and $\$1$ coins. In total, there are $35$ coins that add up to a value of $\$26$. How many coins of each type are in the piggy bank? (Hint: if you call $x$ the number of $\$1$ coins, the number of $\$0,50$ coins will be $35 - x$).

A gardener wants to fence a rectangular plot with a perimeter of $120$ feet. To make better use of the land, he decided that the length should be twice the width minus $6$ feet. What will be the final dimensions of the plot?

Three siblings, Alex, Bella, and Charlie, want to buy a gift for their parents that costs $\$105$. Alex contributes an amount of money, Bella puts in twice as much as Alex, and Charlie puts in $\$15$ less than Bella. How much money does each one contribute so that they have exactly enough for the gift?