buy two coats for the sum of $77 the product of the purchase is $1440 what is the cost of each coat both the sum and the product must be involved

$32 and $45

i just used guess and check.

lyne you rock thanks taylor

To solve this problem, let's start by setting up two equations based on the given information. Let's assume the cost of the first coat is "x" dollars and the cost of the second coat is "y" dollars.

Equation 1: x + y = 77 (The sum of the costs of both coats is $77)

Equation 2: x * y = 1440 (The product of the costs of both coats is $1440)

Now, we have a system of equations to solve simultaneously. There are various methods to solve such systems, but let's use substitution method here:

From Equation 1, we can rewrite it as:
x = 77 - y

Now, substitute this value of x in Equation 2:
(77 - y) * y = 1440

Expanding this equation:
77y - y^2 = 1440

Rearranging it:
y^2 - 77y + 1440 = 0

To solve this quadratic equation, we can factor it:
(y - 48)(y - 30) = 0

Now, set each factor equal to zero:
y - 48 = 0 or y - 30 = 0

Solving these equations:
y = 48 or y = 30

If y = 48, substitute this value into Equation 1 to find x:
x + 48 = 77
x = 77 - 48
x = 29

So, if the cost of the first coat is $29 and the cost of the second coat is $48, the sum of both coats is $77, and their product is $1440.