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.