Answer:
a. How many bowls could you glaze?
6 bowls
How many plates could you glaze?
10 plates
b. You want to glaze 5 bowls, and then use the rest for plates.
How many plates can you glaze?
2 plates
How much glaze will be left over?
8/9 of glaze would be left
c. How many of each object could you glaze so that there is no glaze left over? Explain how you found your answer.
4 4/23 bowls and 4 4/23 plates
Step-by-step explanation:
We are told in the question
Number of pints of glaze = 6 pints
Number of pints to glaze a bowl= 7/8 of pint
Number of pints to glaze a plate = 9/16 of a pint
a.
How many bowls could you glaze?
7/8 pint = 1 bowl
6 pints = x
Cross Multiply
x = 6 pints/ 7/8
= 6 × 8/7
= 48/7
= 6.8571428571 bowls
We can only glaze whole numbers of a bowl, hence, we can only glaze 6 bowls
How many plates could you glaze?
9/16 pint = 1 bowl
6 pints = y
y = 6 pints/ 9/16
= 6 × 16/9
= 10.666666667 plates
We can only glaze whole number of a plate, hence, we can only glaze 10 plates
b. You want to glaze 5 bowls, and then use the rest for plates.
1 bowl = 7/8 pints
5 bowls = z
Cross Multiply
z = 5 × 7/8pints
= 4 3/8 pints of glaze would be used for bowls
How many plates can you glaze?
The rest is for plates, hence:
The amount of glaze left for plates is calculated as:
6 pints - 4 3/8
1 5/8 pints of glaze would be left over to glaze plates.
So therefore,
9/16 pints = 1 plate
1 5/8 pints =
= 2 8/9
Hence we can only glaze 2 plates
How much glaze will be left over?
2 8/9 pints - 2 pints
= 8/9 pints of glaze.
c. How many of each object could you glaze so that there is no glaze left over?
We have 6 pints of glaze
Number of pints to glaze a bowl= 7/8 of pint
Number of pints to glaze a plate = 9/16 of a pint
Let the number of each objects be represented by x
7/8 × x + 9/16 × x = 6 pints
= 4 4/23 bowls and 4 4/23 plates
that simplifys down to 
and because fraction simplifications are similar (related to each other) we can concur that these would be too.