Math Question Again :P?

Question

A pail with 40 washers in it weighs 500 grams. The same pail with 20 washers in it weighs 420 grams. How much does the pail weigh?

Answer 1

p = weight of pail
w = weight of washer

p + 40w = 500

p + 20 w = 420

SOLVE the first equation for p
p + 40w = 500 SUBTRACT 40w from both sides
p = 500 - 40w SUBSTITUTE this value into the second equation

p + 20 w = 420
(500 - 40w) + 20w = 420
500 - 20w = 420 SUBTRACT 500 from both sides
-20w = -80 DIVIDE both sides by -20
w = (-80) / (-20)
w = 4

if each washer weighs 4 grams SUBSTITUTE this value into the first equation and SOLVE for p. Then CHECK your answer in the second equation

p + 40w = 500
p + 40(4) = 500
p + 160 = 500 SUBTRACT 160 from both sides
p = 340 ANSWER the pail weighs 340 grams

CHECK by substituting w = 4 and p = 340 in the second equation

p + 20 w = 420
340 + 20(4) = 420
340 + 80 = 420
420 = 420 It checks out

Answer 2

This is a system of equation problem.
Let x = the weight of 1 washer in [grams]
w = weight of the pail.
* is the symbol for multiplication.
So we have
40*x + w = 500 & 20*x + w = 420
Next solve for w of both equations and set them equal.
420 - (20*x) = 500 - (40*x)

solving for x we get x = 4 grams.

now plug that back into 20*x + w = 420 and solve for w
w = 340 grams.

Answer 3

20 washers = 500-420= 80 grams, so 420-80= 340 grams for the pale.

Answer 4

x = weight of a pail, y = weight of washers

x + 40y = 500
40y = 500 - x
y = (500 - x) / 40

x + 20y = 420
20y = 420 - x
y = (420 - x) / 20

(500 - x) / 40 = (420 - x) / 20
(500 - x) / 2 = 420 - x
500 - x = 840 - 2x
x = 340

Answer: A pail weighs 340 grams.

Proof:
y = (500 - 340) / 40
y = 12.5 - 8.5
y = 4

20(4) + 340 = 420
80 + 340 = 420
420 = 420

Answer 5

Pail - P
Each washer - W

P + 40W = 500
P + 20W = 420

Solve the equations simultaneously, to obtain:

P = 340
W = 4

i.e. the pail is 340g, and the washers are 4g each

Answer 6

to function fractions we ought to constantly have a similar denominator. to try this we ought to multiply the precise and the backside by utilising 5 to get 15/25. I have been given 5 by utilising going 25/5. Then we are able to upload the two fractions to get 36/25. If the thought-approximately multiplying the precise and backside seems slightly complicated, evaluate the quantity a million. we are able to write a million as a million/a million good? yet we are able to additionally multiply the precise and the backside by utilising 2 to get 2/2. Or 3 to get 3/3. All of those additionally are equivalent to a million.