Grade 12 System of Equations Word Problems

Grade 12 System of Equations Word Problems

Read each word problem carefully and set up a system of linear equations to solve it. Show all your work.

1. A total of $10,000 is invested in two funds. One fund pays 6% annual interest, and the other pays 8% annual interest. If the total annual interest earned is $720, how much was invested in each fund?

2. A chemist needs to mix a 20% acid solution with a 50% acid solution to produce 60 liters of a 30% acid solution. How many liters of the 20% solution are needed? How many liters of the 50% solution are needed?

Let x be the amount of 20% solution and y be the amount of 50% solution.

Equation 1:  

Equation 2:  

Amount of 20% solution:   liters

Amount of 50% solution:   liters

3. The sum of the ages of a father and his son is 50 years. In 5 years, the father will be three times as old as his son. What are their current ages?

4. A company produces two types of calculators: basic and scientific. The cost to produce a basic calculator is $10, and a scientific calculator is $15. In one day, the company spent $2500 producing 200 calculators. How many of each type were produced?

5. A system of two linear equations can have exactly two solutions.