Creating Equations with Whole Numbers
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Basic Math › Creating Equations with Whole Numbers
Dr. Jones charges a $50 flat fee for every patient. He also charges his patients $40 for every 10 minutes that he spends with him. If Mrs. Smith had an appointment that lasted 30 minutes, how much did she have to pay Dr. Jones?
$170
$90
$120
$200
Explanation
We can express Dr. Jones's rate in a linear equation:
Since Mrs. Smith's appointment lasted 30 minutes, we have 3 10-minute intervals. Then, we can plug in that number into our above equation to find out how much the appointment cost.
What is the solution of 
Explanation
Reduce the second system by dividing by 3.
Second Equation:
Then we subtract the first equation from our new equation.
First Equation:
First Equation - Second Equation:
Left Hand Side:
Right Hand Side:
Our result is:
Jimmy had 
Explanation
Jimmy starts off with $60, and spends $3.50 everyday.
This means that he will have $56.50 after day 1, $53 after day 2, and so forth.
Only one equation satisfies this scenario. The rest are irrelevant.
What is the solution of 
Explanation
We first multiply the second equation by 4.
So our resulting equation is:
Then we subtract the first equation from the second new equation.
Left Hand Side:
Right Hand Side:
Resulting Equation:
We divide both sides by -15
Left Hand Side:
Right Hand Side:
Our result is:
Roman is ordering uniforms for the tennis team. He knows how many people are on the team and how many uniforms come in each box. Which equation can be used to solve for how many boxes 
b = number of students ÷ number of uniforms per box
b = number of boxes ÷ number of uniforms per box
b = number of students x number of uniforms per box
b = number of boxes x number of uniforms per box
b = number of students - number of uniforms per box
Explanation
The total number of uniforms needed equals the number of students divided by the number of uniforms per box.
What is the solution of 
Explanation
We first add both systems of equations.
Left Hand Side:
Right Hand Side:
Our resulting equation is:
We divide both sides by 3.
Left Hand Side:
Right Hand Side:
Our resulting equation is:
What is the solution of 
Explanation
We add the two systems of equations:
For the Left Hand Side:
For the Right Hand Side:
So our resulting equation is:
Divide both sides by 10:
For the Left Hand Side:
For the Right Hand Side:
Our result is:
