If matt has six times as many sitckers as tom. how many stickers dose he have to give tom so they can have 70 stickers each?
tom has x stickers
Matt has 6x stickers
there must have been a total of 140 stickers
x + 6x = 140
7x = 140
x = 20
Tom has 20 and Matt has 120
So Matt has to give 50 of them to Tom
check:
Tom: 20+50 = 70
Matt: 120-50 = 70
Yeahhh
To find out how many stickers Matt needs to give Tom so they can have 70 stickers each, we can set up an equation.
Let's assume Tom has "x" stickers.
According to the given information, Matt has six times as many stickers as Tom, which means Matt has 6x stickers.
To ensure that both Matt and Tom have an equal number of stickers, Matt needs to give some of his stickers to Tom.
If Matt gives "y" stickers to Tom, then Tom will have x + y stickers, and Matt will have 6x - y stickers.
The problem specifies that Matt and Tom should both end up with 70 stickers each. So, we can set up the equation:
x + y = 70 ---(1) (Tom's stickers + the stickers given by Matt equals 70)
6x - y = 70 ---(2) (Matt's stickers - the stickers given to Tom equals 70)
We can now solve this system of equations using the elimination method.
First, we can multiply equation (1) by -1 (or negate it) and rewrite it as:
-x - y = -70 ---(3)
Now, we can add equations (2) and (3):
(6x - y) + (-x - y) = 70 + (-70)
5x - 2y = 0
We now have a new equation: 5x - 2y = 0
At this point, we have two equations:
5x - 2y = 0 ---(4) (derived by adding equations (2) and (3))
x + y = 70 ---(1) (given information)
To solve this system, we can multiply equation (1) by 2:
2(x + y) = 2(70)
2x + 2y = 140 ---(5)
By adding equations (4) and (5), we can eliminate the "y" variable:
(5x - 2y) + (2x + 2y) = 0 + 140
7x = 140
x = 20
Now we know that Tom has 20 stickers.
To find out how many stickers Matt needs to give to Tom, we can substitute the value of "x" into equation (1):
20 + y = 70
y = 70 - 20
y = 50
Therefore, Matt needs to give 50 stickers to Tom so that they can have 70 stickers each.