Question 1201166: Hi
Angie charmaine and Mabel have a certain number of beads together. Angie must give Mabel 11% of what she has so that Mabel will have half of what charmaine has. Angie will then have 85 more than charmaine. If they have 1875 altogether how many beads did Angie have at first.
Thanks
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! i'm not exactly sure how i got it but i think i got it.
let A = the amount that angie had to start with.
let C = the amount that charmaine had to start with.
let M = the amount that mabel had to start with.
you get:
A + C + M = 1875
M + .11A = .5C
A - .11A = C + 85
combine like terms and multiply both sides of the second eqution to get:
A + C + M = 1875
2M + .22A = C
.89A - 85 = C
since they both equal to C, you get:
2M + .22A = .89A - 85
solve for 2M to get:
2M = .67A - 85
multiply both sides of A + C + M = 1875 by 2 to get:
2A + 2C + 2M = 3750
since 2M = .67A - 85, you get:
2A + 2C + .67A - 85 = 3750
since C = 2M + .22A, then multiply both side of that by 2 to get:
2C = 4M + .44A
2A + 2C + .67A - 85 = 3750 becomes:
2A + 4M + .44A + .67A - 85 = 3750
add 85 to both sides of that equtioon to get:
2A + 4M + .44A + .67A = 3835
combine like terms to get:
3.11A + 4M = 3835
since 2M = .67A - 85, thn multiply both sides of that equation by 2 t get:
4M = 1.34A - 170
replace 4M with that in 3.11A + 4M = 3835 to get:
3.11A + 1.34A - 170 = 3835.
combine like terms and add 170 to both sides of that eqution to get:
4.45A = 4005
solve for A to get:
A = 4005 / 4.45 = 900
since C = .89A - 85, replace A with 900 to get:
C = .89 * 900 - 85 = 716.
subce 2M = .67A - 85, replace A with 900 to get:
2M = .67 * 900 - 85 = 518
solve for M to get:
M = 518 / 2 = 259
you have:
A = 900
C = 716
M = 259
A + C + M = 900 + 716 + 259 = 1875, so that checks out ok.
M + .11A = .5C = 259 + .11 * 900 = .5 * 716 which becomes:
259 + 99 = 358 which becomes:
358 = 358, so that checks out ok.
A - .11A = C + 85 becomes:
900 - 99 = 716 + 85 which becomes:
801 801, so that checks out ok.
it appears very strongly that your solution is angie had 900 beads to start with.
we'll do this again using names rather than labels so it's easier to see.
we have, in the beginning:
angie had 900
mabel had 259
charmaine had 716
angie gave mabel 11% of what she had so that mabel will have half as many as charmaine has.
after the transaction:
angie now has 801
mabel now has 358
charmaine has 716
358 is half of 716, so the transaction was good.
after the transaction, angie will be left with 85 more than charmaine.
801 = 716 + 85, confirming that is a true statement because 801 = 801.
it all looks good, so the solution is confirmed.
the solution is that angie started with 900 beads.
once again, the starting totals are:
angie had 900
mabel had 259
charmaine had 716
total for all 3 was 900 + 259 + 716 = 1875
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