Rizul N. answered • 12/24/12

UNC-CH Grad For Math and Science Tutor

**The second of there #s is 8 more than the first, and the third # is 3 less than 3 times the first. If the third # is 15 more than the second, find the three #s.**

This is an excellent question and something you will trip over several times in algebra I, but you will master it at some time, given you have a good mentor and you pay attention to wording. Let's do this one by one.

**Second # (call this Y)**

**Step 1:** 8 more than first # (call this X)

**Step 2:** Think of Y as 8 more jelly beans than X. You know that this means addition.

**Y = 8 + X **

**Third # (call this Z)**

**Step 1:** Fifteen more than the second # (call this Y)

**Step 2: **Think of this as 15 more jelly beans than Y (which we know is 8 more jellybeans than X)

** Z = 15 + Y = 15 + (8 + X)**

**Z = 23 + X**

**Third # (call this Z)**

**Step 1: **3 less than 3 times the first (call this X)

**Step 2: **3 times the first is a number. Times says to multiply so the number is **3X.** Now let's read the rest of the phrase. "3 less than 3X". Less than implies subtraction. So we have 3X jellybeans and we take away 3 from that amount. This means that 3X comes first cause we're taking away from it and so the third # is

** Z = ****3X - 3 **

So we have our definitions for Y and Z in terms of X. Note that we have two equations for Z because we were given information on Z based on the second number and the first number but because the second number is defined in terms of the first number X as well, we had converted that equation in terms of X as well. In order to solve for X, we substitute X + 23 in for Z in the equation Z = 3X -3.

**X + 23 = 3X - 3**

** 26 = 2X**

** 13 = X**

Now we have the first number X solved. Since Z and Y are both expressed in terms of X, so here is the easy part.

For the third #, you can choose any of the two equations to plug in X = 13. You'll receive same answer.

**Z = 3(13) - 3 = 36**

**Y = 8 + 13 = 21**

First number = 13

Second number = 21

Third number = 36

Rizul N.

Hi Bill, I understand that the response was detailed but I always try to provide alternate explanations. Otherwise, my answer would have been the exact same as John's. For the ease of the OP, I have highlighted the important parts in green. This is what I always practice when my reponses are lengthy.

12/26/12

Bill F.

Hi Rizul... I really respect and like your thorough answers - I just hope our students have the patience and desire to make the time and effort to fully read and understand them :-) Bill

12/25/12