1. The document provides 10 word problems involving simultaneous equations, comparison of ratios, elimination methods, and other mathematical concepts. 2. Students are asked to show the steps and solutions for finding unknown variables and values based on the information provided in each problem. 3. The problems cover topics such as investment returns, dividing amounts, travel speeds, ticket sales, ages, integers, and productivity rates.

1. Worksheet for Simultaneous Equation
Name: Rating:
A. Use Substitution Method to finds the unknown variables
1. 3y – x = 5; 2y + x = -10 6. x + y = 9; x – y = 5
2. 4x – y = 8; 2x – 3y = 14 7. 3x + 2y = 13; 2x + 5y = 5
3. y – 4x = -3; 3y + 2x = 5 8. x + 3y = 9; 2x – y = 4
4. 3y – x = 15; 2y + x = -10 9. x + y = -1; 2x + y = -3
5. 3x – 3y = 2; x – 3y = -2 10. x + y = 7; x – 9y = -13
B. Use Comparison Method to find the unknown variables
1. 2(x – y) = 14; x + 2y = -2 2. x – 2y = 1; x + y = 2

2. 3. 2x – 3y = -11; x – y = -4 7. x + 2y = 4; x + y = 2
4. y + x = 7; x – y = -3 8. y – 2 = 0; x + 3 = 0
5. 2x + y = 7; x – 3y = 7 9. 2x – y = 5; x + y = 4
6. x – 4y = 1; x + y = -4 10. x – 2y = 3; 2x – 3y = 4
C. Use Elimination Method to find the unknown variables
1. 5x + 2y = 4; 4x – 3y = 17 5. 2x – y = 5; 4x + y = 4
2. 3x + 2y = 2; 2x + 3y = -2 6. 3x – 4y = -6; 3x + 7y = 60
3. 3x + y = 8; 3x – 2y = 2 7. 3x – 2y = 0; 4x – 2y = 10
4. 3x + 5y = -21; 2x – 5y = 1 8. 2y + x = 2; 3y – x = -7

3. 9. x + y = -4; x – y = -16 10. y – x = 8; y + x = 22
D. Simplify to find the unknown variables
1. 3(x + y) – 4(y – x) = 19; 6. 2 + x/7 = y/4;
4(2x – y) + y = 18 3 + y/5 = x/3
2. 3/5 x + 2/5 y = 1; 7. 3(y – 3) = 2 (x + 2);
2/5 x – 2y = 12 3(x – 2) – 2 v(y + 1) = 0
3. x + y + 1 = 2(y + x); 8. x – 3y = y;
(x – y)/3 = y – x – 4 (x + 4) + (y + 4) = 33
4. 2/3 x = y; 3/5 x – 2/5 y = 1 9. 6(x – y) – 5 = 21; 3(x + y) = 11
5. 4 – (y – 3) = x + 3; 10. x = 3y; ¾ x = 1 + 2y
(10 + x)/3 = 2 + (y – 12)

4. E. Solve the following:
1. Rellie invests P 12, 000. a part of it earns 10% interest annually and the
rest earns 9% interest annually. His annual income from his investments is
P 1, 130. How much is invested at each rate?
2. A man left an amount of P 525, 000 to be divided among his widow, two
sons and one daughter, each son was to receive twice the amount the
daughter would receive, and the widow was to have eight times the
amount each son would receive. How much was the widow’s share?
3. From a common starting position, Willy and Jessica ride their bikes in
opposite directions. Willy rides 2 km per hour faster than Jessica. In 3
hours, the two are 60 km apart. Find the average speed of each?
4. Find two numbers whose difference is 15 and whose sum is 53.
5. Admission prices in Metro pop concert were P20.00 and P50.00. The total
cash in one of the ticket booths was P 9, 550.00. Tickets were sold to 320
people. How many of each kind of tickets were sold?
6. In 3 years, Alex will be 3 times as old as his sister Precy. A year ago, Alex
was 7 times as old as Precy. How old are they now?

5. 7. The sum of the two integers is 51. The larger integer is 3 more than twice
the smaller integer. Find the integer.
8. If the larger integer of 2 numbers is subtracted from 6 times the smaller
number, the result is 20. If twice the larger number is added to 4 times the
smaller, the result is 56. Find the numbers.
9. For P 100, I can buy 4 chicken pies and 12 banana cakes, or 5 banana
cakes and 10 chicken pies. How much does one of each kind cost?
10. In a girls home, three girls work in the embroidery section. Melba and
Laura can finish a table cloth in 9 days, Melba and Elma can finish the
same work in 8 days, while Laura and Elma can finish it in 12 days. Find
how long it will take each girl working alone to finish the work.