Matt has four times as many stickers as David. How many stickers mush Matt give Davis so that they will each have 75 stickers?
I am so bad at these problems, please help!
If they'll each have 75 stickers, they must start with 150 stickers.
x + 4x = 150
5x = 150
x = 30
David had 30 stickers.
30 + n = 150
n = 120
Matt had 120 stickers.
Can you take it from there?
I can, thanks so much!!
You are very welcome.
To solve this problem, we need to set up an equation to represent the given information.
Let's assume that the number of stickers David has is "x".
According to the problem, Matt has four times as many stickers as David, so Matt has 4x stickers.
We need to find out how many stickers Matt must give to David so that they will each have 75 stickers. Let's represent the number of stickers Matt gives to David as "y".
After Matt gives y stickers to David, David will have x+y stickers, and Matt will have 4x-y stickers.
According to the problem, both of them should have 75 stickers after the exchange. So, we can set up the following equation:
x + y = 75 (equation 1)
4x - y = 75 (equation 2)
Now we have a system of equations. We can solve it to find the values of x and y.
To solve this system of equations, we can use the method of substitution or elimination.
Let's use the substitution method:
From equation 1, we can express y in terms of x:
y = 75 - x
Substitute this value of y into equation 2:
4x - (75 - x) = 75
4x - 75 + x = 75
5x - 75 = 75
5x = 150
x = 30
Now, substitute the value of x back into equation 1 to find y:
30 + y = 75
y = 75 - 30
y = 45
So, David currently has 30 stickers, and Matt has 4(30) = 120 stickers.
To find out how many stickers Matt should give to David so that they each have 75 stickers, we subtract their current number of stickers from 75:
Matt gives David: 120 - 75 = 45 stickers
Therefore, Matt must give David 45 stickers in order for both of them to have 75 stickers.