4 word problems.Help is appreciated.Thanks?

Question

1. The sum of 3 consecutive odd numbers is 39.

2. The Perimeter of a rectangle is 600. The length of the rectangle is 2 more than 3 times the width.

3. Mrs. Gardner went to the market. She purchased some lettuce heads and some tomatoes. There were 12 items purchased. She bought twice as many tomatoes as lettuce heads.

4. 3 times the first of three consecutive numbers is 4 more than 2 times the second

Answer 1

I'll get these done for you.

1) 11 +13 +15 = 39

Let the odd number be represented by N.

N + (N+2) +(N+4) = 39

3N +6 = 39

3N = 39 – 6

3N = 33

N = 33/3

N = 11

a)the first number is 11;

b)the second number is 13; (11+2)

c)the third number is 15; (11+4)

2) The width is 3W and the length is 2 more then that so the length has to be 3W + 2

Perimeter is the sides added together so or  2( l + w)

2 (3W +2 + W) = 600

2 (4W +2) = 600

8W +4 = 600

8W = 600 – 4

8W = 596

W = 596/12

W = 74.5

L = 3W+2

L = (3 x 74.5) +2

L = 225.5

PROOF

Perimeter is

2 (L + W) = 600

2 (225.5 + 74.5) = 600

2(300) = 600

600 = 600

3) Let L represent the number of heads of lettuce .

She bought 2 times as many tomatoes so tomatoes must be 2L.

L + 2L = 12

3L = 12

L = 12/3

L = 4

She bought 4 heads of lettuce and 8 tomatoes.

4 + 8 = 12

4) This one is a lot more difficult to explain. Here is the answer and I'll try to tell you how I got the answer.

The consecutive numbers are 6,7 and 8.

Let the first number be N, so the second number must be N+1;

Three times the first number minus 4 must be equal to 2 times the second number.

3N – 4 = 2(N+1)

3N = 2(N+1) +4

3N = 2N + 2 + 4

3N = 2N + 6

N = 6

consecutive numbers are 6,7 and 8

PROOF

3 times the first number is 4 more that 2 times the second number:

first number is 6: three times the first number 3 x 6 = 18;

second number is 7: 2 x 7 = 14

The first number is 4 more than the second number: 18 is 4 more than 14.

BTW Why are these math questions posted in the geography section???