ACT Math : Linear / Rational / Variable Equations
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Example Questions
Example Question #71 : How To Find The Solution To An Equation
How much water should be added to 
Pure water is 0% and pure solution 100%. Let 
So the equation to solve becomes
and
Example Question #31 : Linear / Rational / Variable Equations
Solve 
This problem is a good example of the substitution method of solving a system of equations. We start by rewritting the first equation in terms of 
Solving this equation gives 
Example Question #43 : Linear / Rational / Variable Equations
Joy bought some art supplies. She bought colored pencils for $1.25 per box and sketch pads for $2.25 each. Joy bought one more sketch pad than colored pencil boxes and spent $9.25. How many sketch pads did she buy?
Let 
So the equation to solve becomes 
Solving this equations leads to 2 colored pencil boxes and 3 sketch pads.
Example Question #35 : Algebra
This question deals with absolute value equations which will normally gives you two solutions.
You need to solve two sets of equations for absolute value problems:
and
Example Question #1811 : Sat Mathematics
Steve sells cars. His monthly salary is $1,000. He gets a $500 commission for each car he sells. If Steve wants to make $7,500 this month, how many cars would he have to sell?
Let 
So
Example Question #37 : Algebra
A chemistry student needs to dilute some acid. How much pure water should be added to 2 gallons of 80% acid solution to yield 20% acid solution?
Let pure water = 0 % and pure acid = 100%
The general equation to use is:
So the equation to solve becomes 
Example Question #41 : How To Find The Solution To An Equation
The Widget Company makes widgets. The monthly fixed costs are $750. It costs $45 to make each widget. The widgets sell for $75 a piece.
What is the monthly break-even point?
The break-even point is where the costs equal revenue.
Let 
Costs:
Revenue:
So the equation to solve becomes
So the break-even point occurs when they sell 25 widgets.
Example Question #41 : Algebra
The Widget Company makes widgets. The monthly fixed costs are $750. It costs $45 to make each widget. The widgets sells for $75 a piece.
The Widget Company wants to make a profit of $3,000. How many widgets must be sold?
Profits = Revenues - Costs
Revenue:
Costs:
Profit:
So the equation to solve becomes
So a $3,000 profit occurs when they sell 125 widgets
Example Question #81 : How To Find The Solution To An Equation
Sally sells custom picture frames. Her monthly fixed costs are $350. It costs $10 to make each frame. Sally sells her picture frames for $35 each.
How many picture frames must Sally sell in order to break even?
The break-even point is where the costs equal the revenues.
Let 
Costs:
Revenues:
Thus,
So 14 picture frames must be sold each month to break-even.
Example Question #82 : How To Find The Solution To An Equation
Sally sells custom picture frames. Her monthly fixed costs are $350. It costs $10 to make each frame. Sally sells her picture frames for $35 each.
To make a profit of $500, how many frames need to be sold?
Let 
Revenues:
Costs:
Profits =
So the equation to solve becomes
So 34 picture frames must be sold to make a $500 profit.
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