Math word problem of my daughters below

Question

What strategy used to find answer?

 

When Malcolm was visiting his Grandpas farm, he saw that the farm only raised hens and hogs. Malcolm counted 38 heads and 100 feet. How many hens and how many hogs did his grandpa have in the barnyard?

Answer 1

Let x = the number of hens and y = the number of hogs.  Each hen and hog has one head, so if there are 38 heads, then:

 

x + y = 30    (so y = 30 - x)

 

Malcolm counted 100 feet.  Hens have 2 feet, hogs have 4, so:

 

100 feet = (2 feet)*(number of hens) + (4 feet)*(number of hogs)

100 = 2x + 4y

 

Now, since y = 30-x, substitute 30-x for y:

 

100 = 2x + 4(30-x)              [Substituted 30-x for y]

100 = 2x + 120 - 4x             [Combine like terms, subtract 120 from both sides]

-20 = -2x

10 = x

 

There are 10 hens and 30-10 = 20 hogs.

 

Check:

100 = 2x + 4y

100 = 2(10) + 4(20)

100 = 20 + 80

100 = 100

Check!