So here you're using system of equations. You can solve systems by graphing, elimination, or substitution. Ill use substitution. First lets solve for x. take the second equation and add y to both sides to get x by itself:
x - y = 75
x = y + 75 now plug y+75 in for x in the first equation
x + y = 743
(y +75) +y = 743 solve for y
2y +75 = 743 subtract 75
2y = 668 divide both sides by 2
y = 334
now plug this into any of the 2 equations to solve for x i chose the second one
x - y = 75
x - 334 = 75 add 334 to both sides
x = 409
This means x, sold before the tournament is 409 and y, sold at the door is 334. That means the assistant is wrong and accidentally flipped the two answers
The formula you can use for the withdrawals is that of an annuity. You have interest adding to the balance at the same time withdrawals are reducing the balance.
The formula I remember for annuities is
.. A = Pi/(1 -(1 +i)^-n) . . . . . i is the interest for each of the n intervals; A is the withdrawal, P is the initial balance.
This formula works when the withdrawal is at the end of the interval. To find the principal amount required at the time of the first withdrawal, we will compute for 3 withdrawals and then add the 7500 amount of the first withdrawal.
.. 7500 = P*.036/(1 -1.036^-3)
.. 7500 = P*0.357616
.. 7500/0.0347616 = P = 20,972.20
so the college fund balance in 4 years needs to be
.. 20,972.20 +7,500 = 28,472.20
Since the last payment P into the college fund earns interest, its value at the time of the first withdrawal is P*1.036. Each deposit before that earns a year's interest, so the balance in the fund after 4 deposits is
.. B = P*1.036*(1.036^4 -1)/(1.036 -1)
We want this balance to be the above amount, so the deposit (P) is
.. 28,472.20*0.036/(1.036*(1.036^4 -1)) = 6510.62
You must make 4 annual deposits of $6,510.62 starting now.
Answer:
Step-by-step explanation:
2a + b = 15.7
2(6.3) + b = 15.7
b = 3.1
2 / (z-5) = z / (0.5z^2 + 7)
cross multiply
z(z - 5) = 2(0.5z^2 + 7) =
z^2 - 5z = z^2 + 14 =
z^2 - z^2 - 5z = 14
-5z = 14
z = -14/5
