SOLUTION: 1)The price of a camera is increased by 40%. later, in a sale, the price is reduced by 20% of its new value. this final price is $50. what was the original price. 2)a)A man pack

Algebra ->  Algebra  -> Finance -> SOLUTION: 1)The price of a camera is increased by 40%. later, in a sale, the price is reduced by 20% of its new value. this final price is $50. what was the original price. 2)a)A man pack      Log On

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Question 92041: 1)The price of a camera is increased by 40%. later, in a sale, the price is reduced by 20% of its new value. this final price is $50. what was the original price.
2)a)A man packed 180 apples in X cartons. write down an expression, in term of X for the number of apples in each carton.
b) Another man packed 160 apples in x+5 cartons write down an expression in terms of X, for the number of apples in each carton.
c) Given that the first man had 4 apples per carton more than the second man, form an equation in X and solve it to find how many apples the first man had in each carton.
Please help me answer these questions.
Answer by ptaylor(1894) About Me  (Show Source):
You can put this solution on YOUR website!
(1)
Let x=original price of camera
If we increase this price by 40%, we would have a new price of (x+0.4x)
If we reduce this new price by 20% we would have (x+0.4x)-((x+0.4x)(0.2)) and we are told that this equals $50. So our equation to solve is:
(x+0.4x)-(x+0.4x)(0.2)=50 get rid of parens
x+0.4x-0.2x-0.08x=50 collect like terms
1.12x=50 divide both sides by 1.28
x=$44.64----------------------original price
CK
($44.64)*0.4=$17.86
$17.86+$44.64=$62.50
$62.50*0.2=12.50
$62.50-$12.50=$50
$50=$50
(2a)
If there are 180 apples in X cartons then each carton contains 180/X apples
CK: (180/X)* Number of Cartons(X)=180
180=180
(2b)
If there are 160 apples in (X+5) cartons the each carton contains 160/(X+5) apples
CK
(160/(X+5))*(X+5)=160
160=160
(2c)
Now we are being told here that
180/X=(160/(X+5))+4 Multiply each term by X(X+5) to get rid of fractions
180(X+5)=160X+4X(X+5) get rid of parens
180X+900=160X+4X^2+20X simplify
180X+900=180X+4X^2 subtract 180X from both sides
180X-180X+900=180X-180X+4X^2 collect like terms
4X^2=900 divide both sides by 4
X^2=225 take square root of both sides
X=+ or - 15 cartons discount negative value
X=15 cartons
180/X=180/15=12------------ apples per carton for first man

Hope this helps---ptaylor