Huzefa K. answered • 04/13/14

Math Teacher|Michigan + Northwestern Law|Perfect Score Math ACT + SAT

**Ky**(K) has 3 times more books than

**Grant**(G), and

**Grant**(G) has 6 fewer books than

**Jamie**(J). if the total number of books is 176, how many books does

**Jamie**(J) have?"

*relationships*. Then, your aim should be to write out expressions that convey those relationships. For example, the first sentence gives us a relationship between

**K**and

**G**, specifically that

**K**has three times more books than

**G**:

**K**= 3

**G**

**G**and

**J**, namely that

**G**has six fewer books than

**J**:

**J**- 6 =

**G**

**K**+

**G**+

**J**= 176

**J**. The problem with this equation is that we have three variables, and we can't solve for three variables. If, however, we can get just one variable, then we can isolate algebraically.

**K**= 3

**G**

**J**- 6 =

**G**

**G**. That is your clue that

**G**is the variable you should be using in the final equation. Therefore, you need to figure out how to represent

**J**and

**K**in terms of

**G**. Here's what you do:

**K**+

**G**+

**J**= 176

**K**(based on

**K**= 3

**G**)

**G**+

**G**+

**J**= 176

**J**; now we need the other relationship, namely

**J**- 6 =

**G**. Isolating for

**J**, we get

**J**=

**G**+ 6. Now substitute:

**G**+

**G**+ (

**G**+ 6) = 176

**G**:

**G**+ 6 = 176

**G**= 170

**G**= 34

**J**- 6 =

**G**

**J**- 6 = 34

**J**= 40

**40 books**. Hope that helped!

Arthur D.

04/14/14