Applications of Linear Equations

The sum of two numbers is . If the larger number is divided by the small number, quotient is , and remainder is . Find the difference of two numbers.

There is a natural number which has 2 digits. The sum of its digits is . The number in which the tens digit and the ones digit are interchanged is greater than the first number. What is the original natural number?

Stella attends a middle school with students. There was a spanish test which has maximum point of . The average point of all the students was . If male students' average is , and average of the females' is , find the difference of number of students between male and female students.

The difference between ages of a father and a daughter is . If the father's age becomes year younger than times of the daughter's age years later. Find the sum of their ages for now.

Hannah paid dollars for boxes of apples and peaches combined. If the price of apple is dollar per box and the price of peaches is dollar per box, how many boxes of apples and peaches has Hannah bought?

Kathie paid dollars for boxes of apples and peaches combined. If the price of apple is dollar per box and the price of peaches is dollar per box, how many boxes of apples and peaches has Kathie bought?

A farm grows animals chickens and pigs combined. If the sum of legs of pigs and chickens is , how many pigs are there in the farm?

Vivian and Victor play rock-paper-scissors game on the stairway. The winner goes up steps, and the loser goes down step. After some time Vivian went steps up from the beginning, and Victor came steps down from the beginning. How many times did Vivian win? (note that they play rock-paper-scissors until someone wins.)

In a quiz competition, if a participants picked a correct answer, points are given while points are taken away if he/she got it wrong. Stephanie participated the competition. The number of wrong answers of hers is of the right anwsers she picked. When her total score was , how many quizes did she had?

For a rectangle, the width is longer than the height. If the perimeter of the rectangle is , find the area of this rectangle.

A school planned to go field trip on application basis. The of male students and female students submitted the applications. If of total students applied and the total number of students is , find the difference between number of male and female students.

There were total admissions to a museum last week. There were less male admissions and more female admissions this week compared to the last week. If the total admissions increased by this week, how many male admissions were there this week?

A merchant bought A product and B product for dollars. If he sold A product with margin, and B with margin. After he sold both products, he made dollars of profit. What was the cost of the product A for which he paid originally?

There is a work that Alexia and Charlie can finish in days together. Because Alexia and Charlie had different schedules, Alexia did the work for the first days and continued by Charlie for the days. What if Charlie had done this work by himself, how many days would it take to complete the work?

Everett climbs up the mountain with the speed of per hour, and comes down from the top with the speed of per hour, which takes hours in total. If the total distance is , find the distance when Everett came down.

Gemma's friend's house is distant from her home. She went there with her kickboard with the speed of per hour. But it was broken in the middle, and she had to walk with the speed of per hour. It took 1 hour and minutes in total. Find the distance that she took the kickboard.

Hannah went from home to the library with the speed of /min. After minutes later that Hannah departed, Clarence followed with the same route by riding a bicycle with the speed of /min. When do they meet after Hannah departed?

Alexia and Luka were far away, and they departed at the same time and met halfway. Alexia walked with the speed of /h, and Luka walked with the speed of /h. Find the distance that Luka walked until they met.

Maribel and Tommy are each spinning at a constant speed on a track with a circumference of . If they start from the same place at the same time and run in the opposite direction, they meet again for the first time in minutes, and if they run in the same direction, they meet again for the first time in minutes. Find out the speed of Maribel. (In this case, Maribel's speed is faster than Tommy's speed.)

It took hours to go up the river at by boat, and hour(s) to go down the river. Find the speed of the ship in the stationary water and the speed of the river, respectively. (However, the speed of the ship and the speed of the river are constant, respectively.)

A train running at a constant speed is passing a bridge of long. It takes minute(s) to completely cross the bridge. And it takes minute to completely pass through a tunnel of . Find the length of the train.

By mixing and of salt water, we made of salt water. Find how much of salt water was used.

There are two salt water and with different concentrations. If we mix of and of , it becomes of salt water. If we mix of and of , it becomes of salt water. In this case, what is the concentration of ?

Food contains of protein, of fat, and food contains of protein and of fat. To obtain protein and fat by dissolving two foods and , how much food is needed?