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.
