Mrs Xu had a total of 227 green plums and red plums. She sold half of the red plums and bought another 40 green ones. As a result, she had equal numbers of green plums and red plums. How many plums of each type did she have at first?
2007-02-11 23:51:08 · 14 answers · asked by bio-nana121 3 in Science & Mathematics ➔ Mathematics
49 green plums and 178 red plums.
Let G = number of green plums originally and R = number of red plums originally.
Mrs Xu had a total of 227 green plums and red plums:
G + R = 227
She sold half of the red plums and bought another 40 green ones so that she had equal numbers of both colors.
So
She now has 40 more green plums, which is G + 40, and she has only half of the red plums now, which is R/2.
Since now she has the same number of each, G + 40 = R/2.
-> 2G + 80 = R
Substitute into original equation:
G + R = 227
G + (2G + 80) = 227
3G = 147
G = 49
So R must be 178.
2007-02-11 23:59:38 · answer #1 · answered by thetunak 4 · 1⤊ 0⤋
Let the number of red plums = x
and let the number of green plums = y
sum of the plums = 227
x + y = 227 -----(1)
After selling half of the red plums, and buying in 40 green ones,
x - (1/2)(x) = y + 40
(1/2)(x) = y + 40
double both side of the equation,
x = 2y + 80 -----(2)
Substitute (2) into (1),
3y + 80 = 227
3y = 147
y = 147/3 = 49
Substitute y = 49 into (2)
x = 2(49) + 80 = 178
Hence, no. of red plums is 178 whereas for green plums, 49.
2007-02-12 00:12:10 · answer #2 · answered by Adrianne G. 2 · 1⤊ 0⤋
Like most word problems of this nature, you'll end up with 2 equations and 2 unknowns to be able to solve.
Let G=green plums
R= red plums
then Mrs. Xu started with
(1) G+R=227
the second equation comes from selling 1/2 the R's and buying 40G's and this sum being equal...
or
(2) R/2 + G + 40 =227
substiture the 1st eq into the second eq and you'll see that she started with 178 Reds and 49 Greens (which adds up to 227).
2007-02-12 00:21:35 · answer #3 · answered by SWH 6 · 1⤊ 0⤋
If Mrs. Xu started with 227 green and red plums, then she started with 49 green plums and 178 red plums.
49+178 = 227
She sold half of her red plums, so she now has 89, and she bought 40 more green plums, so she has 89 of those too.
2007-02-12 00:14:12 · answer #4 · answered by Mathlady 6 · 1⤊ 0⤋
G = green, R = red G=49, R = 178
G + R = 227 <-- with me so far?
(G+40) = R/2 <-- 40 more green, half the red, amounts are equal
2G+80 = R <-- multiply both sides by 2 to isolate R
G + R = 227 <-- the main formula
G + 2G + 80 = 227 <-- replace R with (2G+80)
3G+80 = 227
3G = 147
G = 49 <-- woohoo!
and since G+R = 227, we know that R is 227-49, or 178
2007-02-11 23:59:37 · answer #5 · answered by Anonymous · 2⤊ 0⤋
hey this is simple man
let the green plums be = x
let the red plums be = y
according to question
x+y=227
they have said
he sold half red plums so
now he has y/2 red plums
and he brought 40 more green plums so
he has x+40 green plums
according to question y/2=x+40
compare the equations
u will get 49 green plums and 178 red plums
2007-02-12 00:02:23 · answer #6 · answered by rocker 1 · 0⤊ 1⤋
178 red plums & 49 green plums..
2007-02-12 00:05:17 · answer #7 · answered by pinaakee 2 · 0⤊ 1⤋
227 = G + R
R/2 = G + 40
now solve the simultaneous equations
227 = G + R
227 - R = G
R/2 = G + 40
R/2 = (227 - R) + 40
R = 454 - 2R + 80
3R = 454 + 80
3R = 534
R = 178
227 - R = G
227 - 178 = G
49 = G
2007-02-12 00:00:49 · answer #8 · answered by ♥Tom♥ 6 · 1⤊ 0⤋
49 Green
178 Red
2007-02-11 23:59:20 · answer #9 · answered by Cheesecake King 2 · 0⤊ 1⤋
49 Green 178 Red
Oh some one got it first well now you have at least two right answers
2007-02-12 00:03:32 · answer #10 · answered by kevferg64 3 · 0⤊ 1⤋