Word Problems?

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.

ex: four less than a number
n-4
ex:a number minus five is equal to nine
n-5=9

i dont want the final answer i want the final equation

another EX: The sum of three consecutive even integers is 48 well the final equation is x + (x+2) + (x+4) = 48

Answer 1

1. 11,13,15.
2. l=225, w=75.
3. 8 and 4.
4. 6 and 7.

Answer 2

1. First, you need to represent the three unknown numbers. The first unknown you can call x. Since we are speaking about consecutive odd numbers, the second number will be x+2. The third number will be x+4. Thus you have:
x + (x+2) + (x+4) =39.
Adding up the left side of the equation gives you:
3x + 6 =39.
To isolate the x you need to subtract 6 from each side giving you:
3x = 33
To solve for x you divide each side of the equation by 3, giving you:
x =11

Now, since x=11, x+2 =13 and x+4 =15.

2. A rectangle is four sides. Draw it and label the long sides L and the short sides W. The perimeter is equal to the sum of all sides, or L + L + W + W. The perimeter can also be expressed as 2(W + L). What we want to do now is express L in terms of W. Since we know that the length is 2 more than 3 times the width, we can express L as 3W+2. We also know that the perimeter = 600. Thus we write:
2(W + 3W+2) =600. Now we need to multiply each value within the parentheses by 2, giving us:
2W + 6W + 4 = 600, thus:
8W + 4 = 600, thus:
8W=596
Dividing each side of the equation by 8 gives us:
W= 74.5

Since L = 3W+2:
L= 225.5

3. Start with what you know. You know that Mrs. Gardner purchased a total of 12 items. You don't know how many lettuce heads and how many tomatoes she bought, but you do know that she bought twice as many tomatoes as lettuce heads. Thus you can write the quantity of lettuce heads as L and the quantity of tomatoes as 2L. This gives you:
L + 2L = 12
3L = 12
L = 4
Since she bought 4 lettuce heads and the wuantity of tomatoes is two times the quantity of lettuce heads, you know she bought 8 tomatoes.

4) Since you know the numbers are consecutive, you can express each one in terms of X. The first number is X, the second number is X+1 and the third number is X+2.

The problem tells you that three times the first number, or 3X, is equal to 4 more than 2 times the second, or 2(X+1). Thus you have:
3X = 2(X+1) + 4;
3X = 2X + 2 + 4;
3X = 2X + 6
Solving for X gives you
X = 6
X + 1 = 7
X+ 2 =8

Thus, the numbers are 6, 7 and 8

Answer 3

1)39 = x + (x+2) + (x+4) equals 39 = 3x + 6 so x = 11
if x = 11, then the other two are x+2 = 13 and x+4 = 15

2) P = 2L + 2W and L = 3W + 2
so 600 = 2(3W + 2) + 2W equals 600 = 6W + 4 + 2W = 8W + 4
so 596 = 8W so 74.5 = W
and if W = 71.5 then L = 2 + (74.5 x 3) = 2 + 223.5 = 225.5
so 2 x 225.5 + 2 x 74.5 = 451 + 149 = 600

3) T + L = 12 and T = 2L so 3L = 12 so L = 4 and T = 8

4) 3 x a = 2 x (a + 1) + 4 so 3a = 2a + 2 + 4 = 2a + 6 so a = 6
and if a = 6, then a + 1 = 7 and 3 x 6 = 4 + (2 x 7)

Answer 4

1. 11+13+15=39

2. l=3w+2 w p=600
p=2l+w
600=2(3w+2)+2w
600=6w+4+2w
600=8w+4
596=8w
w=74.5
l=225.5

3. t=2l
12=2l+l
12=3l
4=lettuce
8=tomatoes

4. 6,7,8

Answer 5

1. Guess and check
11+13+15=39

2. l=2(3x)
w=3x
2(3x)+3x=600
6x+3x=600
9x=600
x=66
I think. nots ure