<PRE><B>Question 1187488</B>
let T = the total number of stars in the bottle.
let B = the number of stars that bobby made.
let E = the number of stars that edward made.
let K = the number of stars that kelvin made.


The number of paper stars Bobby made was 21 more than 1/4 the total number of paper stars in the bottle.
the equation for that is B = 1/4 * T + 21.


let R1 equal the remaining stars in the bottle after subtracting what bobby made.
the equation for that is R1 = T - B.
since B = 1/4 * T + 21 then the equation becomes:
R1 = T - (1/4 * T + 21) which becomes:
R1 = 3/4 * T - 21.


The number of paper stars Edward made was 30 more than 1/4 of the remaining number of paper stars in the bottle.
the equation for that is E = 1/4 * R1 + 30.
since R1 = 3/4 * T - 21), the equation becomes:
E = 1/4 * (3/4 * T - 21) + 30 which becomes:
E = 3/16 * T - 21/4 + 30
since 30 = 120/4, the equation becomes:
E = 3/16 * T - 21/4 + 120/4
combine like terms to get:
E = 3/16 * T + 99/4.


let R2 = the the remainder of stars in the bottle after what edward made.
the equation for that is R2 = R1 - E.
since R1 = 3/4 * T - 21, that equation becomes:
R2 = 3/4 * T - 21 - E
since E = 3/16 * T + 99/4, that equation becomes:
R2 = 3/4 * T - 21 - (3/16 * T + 99/4)
simplify that to get:
R2 = 3/4 * T - 21 - 3/16 * T - 99/4
3/4 * T is the same as 12/16 * T
21 is the same as 84/4
R2 = 3/4 * T - 21 - 3/16 * T - 99/4 becomes:
R2 = 12/16 * T - 84/4 - 3/16 * T - 99/4
combine like terms to get:
R2 = 9/16 * T - 183/4.


since R2 was given as being 114, you get:
114 = 9/16 * T - 183/4
add 183/4 to both sides of the equation to get:
114 + 183/4 = 9/16 * T
multiply both sides of the equation by 16 to get:
16 * (114 + 183/4) = 9 * T
simplify to get:
2556 = 9 * T
solve for T to get:
T = 2446 / 9 = 284.


that should be the total number of stars in the bottle.


confirm by repeating the problem with 284 stars in the bottle to see if that solution is good.


the problem statement was:


The number of paper stars Bobby made was 21 more than 1/4 the total number of paper stars in the bottle.
bobby made 1/4 * 284 + 21 = 92
the remaining number of stars was 284 - 92 = 192.


The number of paper stars Edward made was 30 more than 1/4 of the remaining number of paper stars in the bottle.
edward made 1/4 * 192 + 30 = 78
the remaining number of stars was 192 - 78 = 114.


Kelvin made the remaining 114 paper stars.


solution looks good.
bobby made 92
edward made 78
kelvin made 114


total number of stars in the bottle was 92 + 78 + 114 = 284.


it appears that the solution is that they made a total of 284 stars.


i would go with that.



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