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?
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.
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