# Lesson Worksheet: Applications on Systems of Two Linear Equations Mathematics

In this worksheet, we will practice translating a real-life problem into a system of two linear equations and finding its solution.

**Q1: **

Find two numbers with a sum of 42 and a difference of 4.

- A23, 19
- B14, 28
- C26, 19
- D23, 4
- E46, 19

**Q2: **

A man’s age was four times his daughter’s age, 4 years ago. In 5 years, his age will be three times his daughter’s. Find their ages now.

- A8 years, 72 years
- B22 years, 72 years
- C8 years, 76 years
- D22 years, 76 years

**Q3: **

A family are playing on a seesaw at the park. The seesaw is balanced when the father and daughter sit at one end and two brothers sit at the other. The father’s weight is 7 times his daughter’s and the sons have a combined weight of 96 kg. How much does the daughter weigh?

**Q4: **

The length of a rectangle is 6 cm more than its width. If its perimeter is 52 cm, what are its dimensions?

- A20 cm, 10 cm
- B32 cm, 13 cm
- C16 cm, 10 cm
- D16 cm, 22 cm

**Q5: **

Find two numbers with a sum of 42 where one number is one-fifth of the other.

- A8, 42
- B7, 35
- C21, 105
- D14, 70
- E10, 52

**Q6: **

The sum of two numbers is 56. Given that one of the numbers is one seventh of the other, what are the two numbers?

- A7, 42
- B8, 56
- C17, 39
- D8, 42
- E7, 49

**Q7: **

Some girls and boys attend a club. Six times the number of girls at the club is 33 more than the number of boys, and 3 times the number of girls is 33 less than six times the number of boys. How many girls and how many boys attend the club?

- Anumber of girls , number of boys
- Bnumber of girls , number of boys
- Cnumber of girls , number of boys
- Dnumber of girls , number of boys

**Q8: **

In a school competition, students score points for completing long and short puzzles. No points are awarded for incomplete puzzles. Osama scored 85 points for completing 4 long and 5 short puzzles, and Abdullah scored 85 points for completing 3 long and 8 short puzzles. How many points did Hassan score for completing 5 long and 5 short puzzles?

**Q9: **

When the digits of a two digit number are reversed, the result is 27 more than the original number. If the sum of the digits is 9, what was the original two digit number?

**Q10: **

The difference between the measures of the acute angles in a right triangle is . Find the measure of each acute angle.

- A,
- B,
- C,
- D,
- E,