what is the answer to my problems please answer asap

Question

tom is cutting a 56 inch piece of wood and 40 inch piece of wood for shelves  he wants to make the cuts the same length  and also makes sure that there is not any wood left over what is the longest possible length he could cut to make the shelves 

 

Emily needs to buy hot dogs and rolls for a picnic the hot dogs come in packages of 10 the rolls come in packages of 12 what is the smallest amount of hot dogs and rolls  she could buy to have the same number of each 

 

two squares each have sides equal to 5 meters long the two squares are put together to make a rectangle what is the area of the rectangle in square meters 

 

a.20 square meters 

b.100 square meters 

c.25 square meters 

d.50 square meters 

 

Answer 1

For your first question, you're going to want to add up all the wood's length in order to find how out how to cut it without any leftover by finding common multiples of your result. So,

 

56+40=96

 

when you look for common multiples of 96, you get 8 and 12, then you have to find out which of those fit into both the 40 inch piece of wood and the 56 inch piece of wood. One is how long the pieces should be, the other how many pieces you will end up with.

 

 

For your second problem, you should make a chart. Hot dogs on one side, buns on the other. Should look like this...

 

 Packages       Hot dogs         Buns

      1                 8                    10

      2                 16                  20

      3                 24                  30

 

Etc... When the number of hot dogs matches the number of buns in the columns, your answer will be the number of packages in that same row for each.

 

 

Answer 2

The first answer is 8 inches because 8 is the greatest common multiple of 56 and 40. 

 

The second question is 6 packs of hot dogs and 5 packs of rolls will each total 60 hot dogs and 60 rolls.  If you factor both 10 and 12, you need 2 2's (which makes 4), a 5 and a 3 to get the lowest number that is divisible by both 10 and 12. So 4 x 5 x 3 = 60.

 

The answer is d. 50 square meters.  If you put two square with sides 5 meters long together, one side of the rectangle will have 10 meters, so 10 times 5 is 50.