Since the common difference is 6, we can assume that the sequence is arithmetic, with rule
T(n)=6n+5 where T(1)=11
T(9)=6(9)+5=59
<span>Simplifying
4(y + -3) = 6(y + 2)
Reorder the terms:
4(-3 + y) = 6(y + 2)
(-3 * 4 + y * 4) = 6(y + 2)
(-12 + 4y) = 6(y + 2)
Reorder the terms:
-12 + 4y = 6(2 + y)
-12 + 4y = (2 * 6 + y * 6)
-12 + 4y = (12 + 6y)
Solving
-12 + 4y = 12 + 6y
Solving for variable 'y'.
Move all terms containing y to the left, all other terms to the right.
Add '-6y' to each side of the equation.
-12 + 4y + -6y = 12 + 6y + -6y
Combine like terms: 4y + -6y = -2y
-12 + -2y = 12 + 6y + -6y
Combine like terms: 6y + -6y = 0
-12 + -2y = 12 + 0
-12 + -2y = 12
Add '12' to each side of the equation.
-12 + 12 + -2y = 12 + 12
Combine like terms: -12 + 12 = 0
0 + -2y = 12 + 12
-2y = 12 + 12
Combine like terms: 12 + 12 = 24
-2y = 24
Divide each side by '-2'.
y = -12
Simplifying
y = -12</span>
First, we need to add 2/6 and 2/5.
2/6 can be simplified to 1/3
We need to have 1/3 and 2/5 have the same denominator. 3 and 5's LCM (least common multiply) is 15.
Multiply both the numerator and denominator of 1/3 by 5. This equals 5/15.
Multiply both the numerator and denominator of 2/5 by 3. This equals 6/15.
5/15 plus 6/15 is 11/15. This means that Jack's 6000 dollars is 4/15.
Let's say that x is the total amount invested by all three.
6000/x would equal 4/15.
Solve this by multiply 6000 by 15 and 4 by x and making these two equal each other.
90000 would equal 4x. Divide both sides by 4 to get x.
90000 divided by 4 would be 22500.
4/15 is the fraction by Jack
22500 is the total amount invested by all 3
If Aidan can fill 1 potted plant from a full bucket but still have enough left for 3 more, this means Aidan can water 4 plants per full bucket. And if you multiply that 4 by 3 full buckets, it gives you 12, which is the amount of plants 3 full buckets can water.
