Kevin collected 7 times as many rocks as David. When Kevin gave David some of his rocks, they each had 32. How many rocks had Kevin given to David?

Answer 1

David's rocks --- x
Kevin's rocks --- 7x
number of rocks in the exchange --- k

x + k = 32
7x - k = 32
add them
8x = 64
x = 8

so in x + k = 32, 8+k = 32
k = 24

state your conclusion.

Answer 2

K = Kevin's rocks

D = David's rocks

Kevin collected 7 times as many rocks as David means:

K = 7 D

x = number of of rocks that Kevin gave to David

When Kevin gave x rock to David

Kevin have K - x = 7 D - x rocks.

David have D + x rocks.

Each had 32 rocks means.

7 D - x = 32

D + x = 32

The solution of this system of equations is:

D = 8 , x = 24

Kevin given to David 24 rocks.

Check result.

If David have 8 rocks, Kevin have:

7 • 8 = 56 rocks

When Kevin gave 24 rock to David , Kevin have 56 - 24 = 32 rocks.

When Kevin gave 24 rock to David,
David have 24 + 8 = 32 rocks