Word Problems?

Question

Can you solve any of these word problems for me, and if you can, show me how? (easy)
1. The length of a rectangular field is 7 m less than 4 times the width. The perimeter is 136 m. Find the width and length.
2. A sugar Dud has 30 less than twice as many calories as a Krunchy Krum. If 5 sugar Duds have the same number of calories as 8 Krunchy Krums, how any calories are in each?
3. In a week Mike ran 8 km farther than Bill, while Pete ran 1 km less than 3 times as far as Bill. If Pete ran 15 km farther than Mike, how many kilometers did Bill run?

Answer 1

You'll find these problems here
http://www.cs.toronto.edu/~hehner/mathadvice.pdf

Answer 2

1.)
width = w
length = l = 4w - 7
perimeter = p = 2 (w + l) = 2 (w + 4w - 7) = 136
10w - 14 = 136
10 w = 150
w = 150/10
w = 15

l = 4 (15) - 7 = 60 - 7 = 53
p = 2 (15 + 53) = 2 (68) = 136. So answer checks.

2.)
x = calories in Krunchy Krum
2 x - 30 = calories in Sugar Dud
5 (2 x - 30) = 8 x
10 x - 150 = 8 x
2 x = 150
x = 150/2
x = 75

2 x - 30 = 120
5 (120) = 8 (75) ?
600 = 600 ! So our answer is correct.

3.)
x = distance Bill ran
x + 8 = distance Mike ran
(x + 8) + 15 = distance Pete ran = 3 x -1

From the third equation we can find x.

x + 23 = 3 x - 1
22 = 2 x
11 = x

Bill ran 11 kilometers.

Answer 3

Okay-these are 2-equation problems.

number 1:

the length (L) is (=) 7 less than (-7 at the end) 4 times the width (4W), so L=4W-7 is the first equation
the perimeter (2L + 2W) is (=) 136, so 2L+2W=136

L=4W-7
2L+2W=136

use substitution.
2(4W-7)+2W=136
distributive property
8W-14+2W=136
combine like terms
10W-14=136
add 14 to both sides
10W=150
divide by ten on both sides
W=15