ky has 3 times more books than grant,and grant has 6 fewer books than jamie. if the total number of books is 176, how many books does jamie have?

Question

I need help with my algebra. I would like that very much if you could help me.

Answer 1

"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?"

 

Hi Jaya-

Let me try and explain it another way.  The main thing you want to look for with these types of questions are 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 = 3G

 

Next, we see a relationship between between G and J, namely that G has six fewer books than J:

 

J - 6 = G

 

Now we have represented the relationships in equations.  Next, we can set up a third equation with all three variables, which we pull from the final sentence.  It states that all the books add up to 176:

 

K + G + J = 176

 

We will use the last equation to solve for 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.

 

So, can we make this into an equation with one variable?  Yes, by using the relationships we established and then substituting.  This is how you do it:

 

K = 3G
J - 6 = G

 

First, you should notice that both of these relationships contain 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:

 

Take the following equation:

K + G + J = 176 

 

and substitute 3G for K (based on K = 3G)

 

3G + G + J = 176

 

Now you have only two variables.  The next step is to get rid of the J; now we need the other relationship, namely J - 6 = G.  Isolating for J, we get J = G + 6.  Now substitute:

 

3G + G + (G + 6) = 176

 

And now, solve for G:

 

5G + 6 = 176

5G = 170

G = 34

 

And one final substitution, plugging in 34 to the following equation:

 

J - 6 = G

J - 6 = 34

J = 40

 

Jamie has 40 books.  Hope that helped!

Answer 2

n=# of books Jamie has

n-6=# of books Grant has

3(n-6)=# of books Ky has

 

n+(n-6)+3(n-6)=176

n+n-6+3n-18=176

5n-24=176

5n=200

n=40 books  (Jamie)

n-6=34 books (Grant)

3(n-6)=3(40-6)=3(34)=102 books (ky)

40+34+102=176

 

Answer 3

Ky has 3 times more books than Grant,and Grant has 6 fewer books than Jamie. if the total number of books is 176, how many books does Jamie have?

 

Let x = the number of books that Grant has

Let y = the number of books that Ky has

Let z = the number of books that Jamie has

 

We have 3 unknowns, so we need 3 equations:

 

Equation 1: Ky has 3 times more books than Grant   y = 3x

Equation 2: Grant has 6 fewer books than Jamie  x = z - 6

Equation 3: The total number of books is 176   x+y+z=176

 

y = 3x

x = z-6

x+y+z=176

 

Let's substitute z-6 from equation 2 in place of x in equations 1:

 

y = 3x

y = 3(z-6)

y= 3z - 18

 

Now lets substitute z-6 from equation 2 in place of x in equation 3 and 3z-18 in place of y in equation 3:

 

x + y + z = 176

z - 6 + 3z - 18 + z = 176

 

5z = 200

 

z = 40

 

Find x: x = z-6 = 40-6 = 34

Find y: y = 3x = 3(34) = 102

 

(x,y,z) = (32,104,40)

 

Check:

 

x+y+z=176

34+102+40 = 176

176=176