Mary bought 20 bowls and plates for $96. each bowl cost $4.50 and each plate cost $1.50 more than a bowl. she bought more bowls than plates. how many bowls and how many plates did she buy?

This is a system of equation type of problem.

Let x represent the bowls and y represent the plates.

Your equations will be:

4.50x + 6y = 96

x + y = 20

We can solve this problem by either the substitution method or elimination method.

Substitution method:

1) Solve for x.

x + y = 20

x = 20 - y

2) Substitute x with 20 - y in the other equation.

4.50x + 6y = 96

4.50(20 - y) + 6y = 96

3) Distribute the outside term through the terms inside the parenthesis and simplify the rest of the equation.

90 - 4.50y + 6y = 96

90 + 1.50y = 96

1.50y = 6

y = 4

4) Now that we know the numerical value of y, solve for the numerical value of x by substituting once more.

a) x + 4 = 20

x = 16

b) 4.50x + 6(4) = 96

4.50x + 24 = 96

4.50x = 72

x = 16

*The solution is that:

Mary bought 16 bowls and 4 plates.

Idon’t know how to do that

Answer: f(x) = -2x^3 +3x^2 +11x -6see attachedan infinite number. since the magnitude of the leading coefficient is not specified, it may be any negative number. (we have chosen the smallest magnitude integer that makes all coefficients be integers.)step-by-step explanation:

1. when "a" is a root of a polynomial, (x -a) is a factor of it. for the three roots given, the factors of the desired polynomial are (x +2)(x -1/2)(x -3).

in order to make the leading coefficient be negative, we need to multiply this product by a negative number. any negative number will do, but we choose a small (magnitude) value that will eliminate the fraction: -2.

then

f(x) = -2(x +2)(x -1/2)(x -3) = -(x +2)(2x -1)(x -3)

= -(2x² +3x -2)(x -3)

= -(2x³ -3x² -11x +6)

f(x) = -2x³ +3x² +11x -6

2. a graph created by the desmos on-line graphing calculator is shown, and the zeros are highlighted.

3. as indicated in part 1, the multiplier of this equation can be anything and the zeros will remain the same. you want a negative leading coefficient, so the "anything" is restricted to any of the infinite number of numbers that will make that be the case.