SOLUTION: Mrs Parkson buys some oranges from a supermarket. She finds that: I. If she buys a dozen oranges in brand A, she will have $96 left. II. If she buys two dozen oranges in brand B,

Algebra ->  Equations -> SOLUTION: Mrs Parkson buys some oranges from a supermarket. She finds that: I. If she buys a dozen oranges in brand A, she will have $96 left. II. If she buys two dozen oranges in brand B,      Log On


   



Question 1054033: Mrs Parkson buys some oranges from a supermarket. She finds that:
I. If she buys a dozen oranges in brand A, she will have $96 left.
II. If she buys two dozen oranges in brand B, she will use half of the money brought.
Given that the price of each orange in brand B is $1 less than that in brand A, find the original amount that Mrs Parkson has.

Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
x, price of one of brand A
y, price of one of brand B
h, amount of money Mrs. Parkson is holding before any purchase
y=x-1

BUY 12 of brand A, keep $96.
h-12x=96


BUY 24 of brand B, keep h%2F2 dollars.
h-24y=h%2F2
-
h-24%28x-1%29=h%2F2
2h-48%28x-1%29=h
2h-48x%2B48=h
h-48x%2B48=0
h-48x=-48

This makes for a system of equations
system%28h-12x=96%2Ch-48x=-48%29
and you can probably solve this without trouble.


system%284h-48x=384%2Ch-48x=-48%29
-
4h-48x-h%2B48x=384%2B48
.
.
.

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

Mrs Parkson buys some oranges from a supermarket. She finds that:
I. If she buys a dozen oranges in brand A, she will have $96 left.
II. If she buys two dozen oranges in brand B, she will use half of the money brought.
Given that the price of each orange in brand B is $1 less than that in brand A, find the original amount that Mrs Parkson has.
Let original amount she had be D
Then cost of 1 dozen Brand A oranges = D – 96, and cost of 1 Brand A orange is: %28D+-+96%29%2F12
Cost of 2 dozen Brand B oranges = ½D, or D%2F2, & cost of 1 Brand B orange = matrix%281%2C3%2C+%28D%2F2%29%2F24%2C+or%2C+D%2F48%29
We then get: %28D+-+96%29%2F12+=+D%2F48+%2B+1
4(D – 96) = D + 48 ------- Multiplying by LCD, 48
4D – 384 = D + 48
4D – D = 48 + 384
3D = 432
D, or original amount she had was: highlight_green%28matrix%281%2C3%2C+432%2F3%2C+or%2C+%22%24144%22%29%29