A mint has three machines capable of making coins. All three machines together can make 246 coins per minute. Machine A is twice as fast as machine B. Machine C can make 30 more coins per minute than machine B. How many coins per minute can machine B make?
2007-09-14 14:40:19 · 4 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
54
Assume Machine B makes x coins per minute.
Then A makes 2x per minute, and C makes x+30 per minute.
So x + 2x + (x+30) = 246
4x+30 = 246
4x = 216
x = 54
So B makes 54 coins per minute.
2007-09-14 14:45:08 · answer #1 · answered by jenh42002 7 · 0⤊ 0⤋
Take what you know...
A = 2B
C = B + 30
A + B + C = 246
Now it is just a case of plugging in the values for A and C and solving for B.
(2B) + B + (B + 30) = 246
4B + 30 = 246
4B = 216
B = 54
Now go the other direction and solve for A and C
A = 2B = 108
C = B + 30 = 84
B = 54
Add it all up and you get 246.
It helps to write out what you know so you can visualize the figures. (There is no need to bring in yet ANOTHER letter. Also, "X" is a bad letter to use as it some times gets mistaken for the multiplication sign.)
2007-09-14 14:48:17 · answer #2 · answered by forgivebutdonotforget911 6 · 0⤊ 0⤋
a+b+c=246
a=2b
c=b+30 => add last two equations and substitute for a+c=3b+30 in first equation
4b+30=246 => 4b=246-30=216 => b=216/4=54 So a=108 and c=84
does a+b+c=246?
108+54+84=108+138=246 Yes!
2007-09-14 14:50:26 · answer #3 · answered by oldschool 7 · 0⤊ 0⤋
A+B+C=246
A=2B
C=B+30
(2B)+B+(B+30)=246
4B+30=246
4B=216
B=54
A=2B
A=2(54)
A=108
C=B+30
C=54+30
C=84
2007-09-14 15:04:25 · answer #4 · answered by Emily L 1 · 0⤊ 0⤋