example
A college student earned $7000 during summer vacation working as a waiter at a popular restaurant. The student invested part of the money at 10% and the rest at 5%. If the student received a total of $500 in interest at the end of the year, how much was invested at 10%?
a) Identify the unknowns and assign a variable to each.
b) Use the variables from Part (a) and write a system of two equations to the model the problem.
c) Solve the system BY HAND (show your work using elimination or subtraction.
d) Answer the original question in the problem in a complete sentence.
Solution
a) The problem involves two investments, one invested at 10% and the other invested at 5%.
|
X: $ invested at 10%
Y: $ invested at 5% |
The ordered pair we get is (3000,4000)
d) The college student invested $3000 at 10% interest.
EQUATION, TABLE, AND GRAPH
Reflection
This example is about how much a college student has invest from money he/she has earned from a summer job at a popular restaurant. The variables that we know were given in the word problem itself. We know that the college student had invest part of the money at 10% and the rest at 5% and has received a total of $500 in interest at the end of the year. We want to know how much he/she had invested at 10%. We then assign variables to the unknown 'X' or 10% and 'Y' for 5%. We also use the system of equations to find the values of the variables. System of equations is a collection of two or more equations with a same set of unknowns in solving a system of equations, we try to find values for each of the unknowns that will satisfy every equation in the system. This word problem is a fair difficulty since you have to plot out what variables are assigned to what values and solve the 'X' and 'Y' as you go. The graph displays how much money was invest at 10% and 5%. Overall the word problem is another good step for getting well verse with dealing more advance problems with more variables.