Mary has a third of the money Erin has. Erin has $8 less than John. Together they have $267. How much money does each of them have?
Mary=1/3*(x-8),Erin=(x-8),John=x
1/3*(x-8)+(x-8)+x=267
take the L.C.M=3
(x-8)+3(x-8)+3x=267*3
Remove brackets
x-8+3x-24+3x=801
Collect like term
x+3x+3x-8-24=801
7x-32=801
7x=801+32=833
X=833/7=119
Mary=1/3 (119-8)=37
Erin=119-8=111
John=119
Check:37+111+119=267
lol xd
Mary=1/3*(x-8),Erin=(x-8),John=x
1/3*(x-8)+(x-8)+x=267
take the L.C.M=3
(x-8)+3(x-8)+3x=267*3
Remove brackets
x-8+3x-24+3x=801
Collect like term
x+3x+3x-8-24=801
7x-32=801
7x=801+32=833
X=833/7=119
Mary=1/3 (119-8)=37
Erin=119-8=111
John=119
Check:37+111+119=267
To solve this problem, let's break it down into smaller parts.
Let's start by representing how much money Erin has. According to the given information, Erin has $8 less than John. Let's assume John has 'x' dollars, then Erin has 'x - $8' dollars.
Now, we are also told that Mary has a third of the money Erin has. So if Erin has 'x - $8' dollars, Mary has '(1/3)*(x - $8)' dollars.
Finally, we are given that together they have $267. So we can set up the following equation:
John's money + Erin's money + Mary's money = $267
x + (x - $8) + (1/3)*(x - $8) = $267
Now we can solve this equation to find the values of x, Erin's money, and Mary's money.
Combining like terms:
x + x - $8 + (1/3)*(x - $8) = $267
2x - $8 + (1/3)*(x - $8) = $267
Multiplying both sides by 3 to clear the fraction:
3*(2x - $8) + (x - $8) = 3*$267
6x - $24 + x - $8 = $801
Combining like terms:
7x - $32 = $801
Adding $32 to both sides:
7x = $833
Dividing both sides by 7:
x = $119
So, John has $119. Now we can find Erin's money:
Erin's money = x - $8 = $119 - $8 = $111
And finally, we can find Mary's money:
Mary's money = (1/3)*(x - $8) = (1/3)*($111) = $37
In conclusion, John has $119, Erin has $111, and Mary has $37.
More money than me:).
I’m just kidding!