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Solve each problem.

1.) Find four consecutive integers whose sum is 246.
2.) One number is four times the other number. If their is 80, find the numbers.
3.) Adams is 20 years younger than Brian. In two years, Brian will be twice as old as Adam. How old are they now?
4.) Seven more than a number added to the same number results to twenty-three. Find the number.

User Jbakirov
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1 Answer

5 votes

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.

User Dobz
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