you buy two coats the sum is $77 the product of your purchase is $1440 how much is each coat
Each coat is $38.50
What does the purchase of the product have to do with the sum Then divide 77 by 2 and it comes to 38.50.
the product is the second part of the question help
To determine the price of each coat, let's assign variables to the unknowns. Let's say one coat costs x dollars, and the other coat costs y dollars.
From the information given, we have two equations:
Equation 1: x + y = 77 (the sum of the two coats is $77)
Equation 2: x * y = 1440 (the product of the two coats is $1440)
To solve this system of equations, we can use the substitution method:
1. Rearrange Equation 1 to express one variable in terms of the other:
x = 77 - y
2. Substitute the expression for x in Equation 2:
(77 - y) * y = 1440
3. Expand the equation:
77y - y^2 = 1440
4. Rearrange and rewrite the equation in standard quadratic form:
y^2 - 77y + 1440 = 0
5. Solve the quadratic equation using factoring, completing the square, or the quadratic formula. However, in this case, the equation easily factors as:
(y - 45)(y - 32) = 0
6. Set each factor equal to zero to find the possible values of y:
y - 45 = 0 --> y = 45
y - 32 = 0 --> y = 32
We have two possible solutions for y, which represent the prices of the two coats.
If y = 45, substitute this value into Equation 1:
x + 45 = 77
x = 77 - 45
x = 32
So, one coat costs $32 and the other coat costs $45.
If y = 32, substitute this value into Equation 1:
x + 32 = 77
x = 77 - 32
x = 45
Therefore, the other possible solution is one coat costing $45 and the other coat costing $32.