Table A and Table B

Question

A store has two rectangular tables. Table A and Table B. The length of table A is 6 2/3 feet, and its width is 3 1/2 feet. The length of table B is 4 1/4 feet. Both tables have the same area

 

Part A: Write an expression that can be used to find the width, in feet, of Table B

 

Part B: What is the width, in feet, of Table B? Show your work and write that answer as a mixed number

Answer 1

Area of a rectangle is length times width, so Table A's area would be 6 2/3 * 3 1/2.  If you can't use a calculator, then the best way to solve this is to convert both mixed numbers into improper fractions.

6 2/3 becomes 20/3  and 3 1/2 becomes 7/2.  Now they're much easier to multiply.

20/3 * 7/2 = 140/6 which can be reduced to 70/3.  For now, we'll keep it as an improper fraction.

 

Part A:

We also need to change 4 1/4 into an improper fraction, so it becomes 17/4.  Now set up your area equation for Table B.  Length is 17/4, width is x, and area is 70/3 (it's the same area as Table A).

 

17/4 * x = 70/3

 

Part B:

Now we need to actually solve for x from Part A.

If we multiply both sides by 4/17, we can get x by itself (17/4 * 4/17 = 1)

 

x = 70/3 * 4/17

 

x = 280/51

 

x = 5 25/51 ft