Ky has 3 times more books than Grant, and Grant has 6 fewer books than Jaime. If the total combined number of books is 176, how many books does Jaime have?
k = 3g
g = j-6, so j = g+6
k+g+j = 176
3g + g + g+6 = 176
5g= 170
g = 34
k = 102
j = 40
58
Let's represent the number of books Jaime has as J.
According to the problem, Grant has 6 fewer books than Jaime, so Grant has J - 6 books.
And Ky has 3 times more books than Grant, so Ky has 3 * (J - 6) = 3J - 18 books.
The total combined number of books is given as 176, so J + (J - 6) + (3J - 18) = 176.
Combining like terms, we get 5J - 24 = 176.
Adding 24 to both sides of the equation, we get 5J = 200.
Dividing both sides of the equation by 5, we get J = 40.
Therefore, Jaime has 40 books.
To solve this problem, let's break it down step by step:
Step 1: Let's assign variables to the unknowns in the problem.
- Let x represent the number of books Jaime has.
- Since Grant has 6 fewer books than Jaime, Grant's number of books would be x - 6.
- Ky has 3 times more books than Grant, so Ky's number of books would be 3 * (x - 6).
Step 2: Write an equation to represent the problem.
The total combined number of books is given as 176, so we can write the equation:
x + (x - 6) + 3 * (x - 6) = 176
Step 3: Simplify and solve the equation.
Start by simplifying the equation:
x + x - 6 + 3x - 18 = 176
5x - 24 = 176
Next, solve for x:
5x = 176 + 24
5x = 200
x = 200 / 5
x = 40
Step 4: Determine the number of books Jaime has.
From our equation, we found that x = 40, so Jaime has 40 books.
Therefore, the number of books Jaime has is 40.