Question

Need help with these 2 problems. Please help me!

The sum of two numbers is 41. The larger number is 1 more than 4 times the smaller number. What are these numbers?


Mrs. henry has 36 feet of fencing, which she plans to install to form a square-shaped yard for her dog. if the back of her house becomes one side of the square with the other sides requiring fencing, how long should each side be?

Answer 1

larger=33 smaller = 8

Step-by-step explanation

41=x+(4x+1)

41=5x+1

41-1=5x-1

40=5x

x=8

Answer 2

1. The numbers are 8 and 33
2. Each side should be 12 ft

Explanation:

These problems can be solved using your knowledge of times tables and by reasoning. You don't need equations (which only serve to formalize the reasoning).

1. If you subtract 1 from the larger number, the total is 40 and the larger number is exactly 4 times the smaller. That makes the total of the two numbers 5 times the smaller, so the smaller is 40/5 = 8. The larger is 41-8 = 33. (Check: 33 = 4·8 +1.)

___

2. The 36 ft of fence will be used to form three equal-length sides of the dog yard. Those sides must be (36 ft)/3 = 12 ft in length.