After mastering linear equations in one variable, the next step is to learn how to tackle real world problems. These are known as application problems or word problems. These problems require us to cipher through key information and create and solve an equation to gain our answer.
Test Objectives:•Demonstrate the ability to find the main objective in a word problem
•Demonstrate the ability to setup an equation when solving a word problem
•Demonstrate the ability to report the answer and ensure the result is reasonable
Applications of Linear Equations I:
#1:
Instructions: Solve each word problem.
a) A piggy bank contains nickels, dimes, and quarters only. There are twice as many quarters as dimes, but only half as many nickels as dimes. The total value of the piggy bank is $11.25. How many quarters, dimes, and nickels are in the piggy bank?
#2:
Instructions: Solve each word problem.
a) Jacob inherited some money from his father. He deposited part of the money in a savings account paying 7% annual simple interest, and $40,000 less than that amount in a different account paying 13% annual simple interest. The annual income from both accounts is $8800. How much was invested at each rate?
#3:
Instructions: Solve each word problem.
a) A drug store clerk counts her cash register and finds that she has 10’s, 20’s, and 100’s only. There are five times as many 20’s as 10’s and one - quarter the amount of 100’s as 20’s. The total value of all bills is $2820. How many 10’s, 20’s, and 100’s were in the register?
#4:
Instructions: Solve each word problem.
a) The owner of a sandwich shop found that the orders on Monday for ham and cheese sandwiches were double that of turkey and one - half that of chicken. If 70 total sandwiches were sold between these three types, how much of each type of sandwich was sold?
#5:
Instructions: Solve each word problem.
a) Three siblings Jane, Bernie, and Ralph are different ages. Bernie is six years younger than Jane, and six years older than Ralph. If the combined age of the three is 54, how old is each person?
Written Solutions:
Solution:
a) There are 18 dimes, 36 quarters, and 9 nickels in the piggy bank.
Solution:
a) $70,000 was invested at 7%, and $30,000 was invested at 13%.
Solution:
a) There were sixty 20 dollar bills, along with twelve 10 dollar bills, and fifteen 100 dollar bills.
Solution:
a) The sandwich shop sold 20 ham and cheese sandwiches along with 10 turkey sandwiches, and 40 chicken sandwiches.
Solution:
a) Jane is 24 years old, while Bernie is 18 years old, and Ralph is 12 years old.