Answer:
1. To find four consecutive integers whose sum is 246, we can set up an equation. Let x be the first of the four consecutive integers. Then the next three consecutive integers are x+1, x+2, and x+3. The sum of these four integers is 246, so we have:
x + (x+1) + (x+2) + (x+3) = 246
Simplifying and solving for x, we get:
4x + 6 = 246
4x = 240
x = 60
Therefore, the four consecutive integers are 60, 61, 62, and 63.
2. Let one number be x and the other number be 4x (since one number is four times the other). Then we have:
x + 4x = 80
5x = 80
x = 16
Therefore, one number is 16 and the other number is 4 times 16, which is 64.
3. Let Adam's age be x. Then Brian's age is x+20 (since Adam is 20 years younger than Brian). In two years, Brian's age will be twice as old as Adam's age, so we have:
(x+20+2) = 2(x+2)
Simplifying and solving for x, we get:
x+22 = 2x+4
x = 18
Therefore, Adam is 18 years old and Brian is 38 years old.
4. Let the width of the rectangle be x. Then the length is 4x+1 (since the length is one centimeter more than four times the width). The perimeter of the rectangle is the sum of the four sides, which is:
2(width + length) = 92
Substituting in the expressions for width and length, we get:
2(x + 4x + 1) = 92
Simplifying and solving for x, we get:
10x + 2 = 92
10x = 90
x = 9
Therefore, the width is 9 cm and the length is 4(9)+1 = 37 cm.