All SAT Math Resources
Example Questions
Example Question #31 : Algebra
If is defined for all numbers and to be , then what is ?
In evaluating, we can simply plug in 4 and 2 for and respectively. We then get .
Example Question #34 : How To Find The Solution To An Equation
Internet service costs $0.50 per minute for the first ten minutes and is $0.20 a minute thereafter. What is the equation that represents the cost of internet in dollars when time is greater than 10 minutes?
The first ten minutes will cost $5. From there we need to apply a $0.20 per-minute charge for every minute after ten. This gives
.
Example Question #32 : Algebra
John goes on a trip of kilometers at a speed of kilometers an hour. How long did the trip take?
If we take the units and look at division, will yield hours as a unit. Therefore the answer is .
Example Question #1809 : Act Math
With a head wind a plane can fly a certain distance in five hours. The return flight takes an hour less. How fast was the plane flying?
In general, .
The distance is the same going and coming; however, the head wind affects the rate. The equation thus becomes .
Solving for gives .
Example Question #31 : Algebra
How much water should be added to of 90% cleaning solution to yield 50% cleaning solution?
Pure water is 0% and pure solution 100%. Let = water to be added.
in general where is the volume and is the percent.
So the equation to solve becomes
and
Example Question #1811 : Sat Mathematics
Solve and
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 to get and then substutite the into the second equation to get
.
Solving this equation gives and substituting this value into one of the original equations gives , thus the correct answer is .
Example Question #41 : How To Find The Solution To An Equation
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 = # of color pencil boxes and = # of sketch pads purchased.
So the equation to solve becomes .
Solving this equations leads to 2 colored pencil boxes and 3 sketch pads.
Example Question #212 : 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 #32 : Algebra
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 = money earned and = number of cars sold
So
and solving shows that he needs to sell 13 cars to make $7,500.
Example Question #141 : 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:
where is the volume and is the percent solution.
So the equation to solve becomes and gallons of pure water needs to be added to get a 20% acid solution.