0Wordy Problems:
The concepts of linear equations in 1 variable and 2 variables generally are tested in wordy questions on the SAT. The equations are generally translations of wordy situations in the questions. Translating the wordy questions to mathematical equations is generally tricky on the SAT.
Example: If twice a number is three less than itself, what is nine more than three times the number?
Solution:
Such wordy questions are better dealt in parts:
Firstly, assume the number to be x
Then, twice the number would be 2x
Three less than itself would be x-3
Given both are equal 2x = x-3
Solving, x = -3
However, three times the number would be 3*-3 = -9
And, nine more than it would be 9+-9 = 0
Hence, the answer is 0
The math part on the right column of the above solution is all simple solving of a linear equation in 1 variable.
The wordy part on the left column of the above solution is all translating the wordy questions part by part into mathematical expressions/equations, which is what makes the simple math a bit more challenging on the SAT.
Example: If the price of 3 type A pencils less than the price of 2 type B pencils equals $1 and a set of 2 type A pencils and 3 type B pencils costs $8, what is the price of a type A pencil?
Solution:
Solving a pair of linear equations in 2 variables: 2y-3x=1, 3y+2x = 8 would give the answer.
How are the equations formed out of the wordy questions is what the SAT is testing one on.
So let’s understand the same:
Firstly, assuming the price of one type A, type B pencil to be $x, $y respectively, And then, the price of 3 type A pencils would be 3 times x = 3x
The price of 2 type B pencils would be 2 times y = 2y
Also, the price of 3 type A pencils less than the price of 2 type B pencils would be = 2y-3x
Given, equals $1. Hence, 2y-3x=1
Similarly converting the information into equations we get another equation in 2 variables, 2x+3y = 8.
To get the price of a type A pencil, we can simply solve for x using the pair of equations derived above. x, y turn out to be 1 and 2 respectively.
You may try:
Albert’s and Benjamin’s ages add up to 35 years now. If Albert is twice as old as Benjamin was when Albert was as old as Benjamin is now, then how old is Albert?
