SOLUTION: Hi Shop p had 200 apples and 300 oranges. Shop q had 240 apples and 100 oranges. How many apples and oranges must be moved from q to p so that half of the fruits in p and 3/4 of t

Question 1200905: Hi
Shop p had 200 apples and 300 oranges. Shop q had 240 apples and 100 oranges. How many apples and oranges must be moved from q to p so that half of the fruits in p and 3/4 of the fruits in q are apples in the end.
Thanks
Found 2 solutions by Theo, greenestamps:
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
p had 200 apples and 300 oranges.
q had 240 apples and 100 oranges.
total number of fruits in p is 500.
total number of fruitis in q is 340.
let x = the number of apples to be moved from q to p.
let y = the number of oranges to be moved from q to p.
when all is said and done, you want half of the fruits in p and 3/4 of the fruits in q to be apples.
you have 2 equations that need to be solved simultaneously.
they are:
200 + x = .5 * (500 + x + y)
240 - x = .75 * (340 - x - y)
simplify to get:
200 + x = 250 + .5 * (x + y)
240 - x = 255 - .75 * (x + y)
subtract 200 from both sides of the first equation and subtract .5 * (x + y) from both sides of the first equation to get:
x - .5 * (x + y) = 50
subtract 240 from both sides of the second equation and add .75 * (x + y) to both sides of the second equation to get:
.75 * (x + y) - x = 15
the two equations that need to be solved simultaneously are:
x - .5 * (x + y) = 50
.75 * (x + y) - x = 15
simplify and combine like terms in both equaations to get:
.5x - .5y = 50
-.25x + .75y = 15
multiply both sides of the second equation by 2 and leave the first equqtion as is to get:
. 5x - .5y = 50
-.5 x + 1.5y = 30
add the two equations together to get:
y = 80
replace y with 80 in the first equqtion to get:
.5x - .5*80 = 50
simplify to get:
.5x - 40 = 50
solve for x to get:
x = 180
your solution should be x = 180 and y = 80
shop p started with 200 apples and 300 oranges.
add 180 apples and 80 oranges to get 380 apples and 380 oranges.
the number of apples is 50% of the total for shop p.
shop q started with 240 apples and 100 oranges
subtract 180 apples and 80 oranges to get 60 apples and 20 oranges.
the number of apples is 75% of the total for shop q.
your solution appears to be:
180 apples and 80 oranges are moved from q to p.

Answer by greenestamps(13203) (Show Source): You can put this solution on YOUR website!

let x = # of apples moved from q to p
let y = # of oranges moved from q to p

After the move, we have

200+x apples in p
240-x apples in q
300+y oranges in p
100-y oranges in q

After the move, half of the fruits in p are apples, so the number of apples in p is the same as the number of oranges in p. And after the move, 3/4 of the fruits in q are apples, so the number of apples in q is 3 times the number of oranges in q.

200+x = 300+y
240-x = 3(100-y) = 300-3y

One method for solving the pair of equations is to solve the first equation for y and substitute in the second equation.

y = x-100
240-x = 300-3(x-100)
240-x = 600-3x
2x = 360
x = 180
y= 180-100 = 80

ANSWER: move x = 180 apples and y = 80 oranges from q to p

CHECK:

apples in p at the end: 200+180 = 380
oranges in p at the end: 300+80 = 380
half the fruits in p are apples

apples in q at the end: 240-180 = 60
oranges in q at the end: 100-80 = 20
3/4 of the fruits in q are apples

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