SOLUTION: For every positive 2-digit number, x, with tens digit t and units digit u, let y be the 2-digit number formed by reversing the digits of x. Which of the following expressions is eq

Question 550039: For every positive 2-digit number, x, with tens digit t and units digit u, let y be the 2-digit number formed by reversing the digits of x. Which of the following expressions is equivalent to x-u? my act answer key had f but i have no clue how it got that answer so an answer with work would be much appreciated! thank you very much and happy new year!
f.9(t-u)
g.9(u-t)
h.9t-u
j.9u-t
k.0

Answer by fcabanski(1391) (Show Source): You can put this solution on YOUR website!
It appears the problem is mis-written as find x-u. Here is the correct problem: "For every positive 2-digit number, x, with tens digit t and units digit u, let y be the 2-digit number formed by reversing the digits of x. Which of the following expressions is equivalent to x-y?"

Here is how to solve it on the ACT.

To solve math on the ACT follow a five step process. Identify the problem type. Set Up (generally by writing what you are given 0). Make sure that you have all the numbers and information correct. Execute - solve the problem. Make sure again that you have answered what was asked.

Identify this problem as a Backsolve problem. A Backsolve problem on the ACT is one which has variables in the problem and either numbers or variable expressions in the solution. As soon as you identify a problem as a backsolve, follow these steps.

1. Pick numbers for the variables in the problem. Pick variables that fulfill the specs set in the problem. This problem indicates that for every positive integer X with tens T and units U, let X be TU and y be UT. Pick the easiest numbers you can imagine for the situation. T=1, U=2. Thus X=12 and Y=21.

2. With the numbers you picked, perform the operations specified in the problem. It asks you to find X-Y which is 12 - 21 = -9.

3. Plug your numbers into each solution until you find the one that results in the same answer as found in step 2. In this problem, look for the expression that results in -9.

Checking F: 9*(1-2) = 9*-1 = -9. F is the answer.

For digits problems pick different non 0 numbers for the digits. Don't pick the same numbers for the digits, or 0 for one of them, unless the problem specifies it such as "one of the digits is 0" or "both digit are the same". Check what happens if you make one of the digits 0, or both the same. Note that F is valid in both cases, but more than one of the answer choices work.

I tutor ACT prep. Contact me if you'd like tutoring to improve your score.

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