A mint has three machines captable 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?
2007-07-12 15:59:08 · 5 answers · asked by *05* 1 in Science & Mathematics ➔ Mathematics
Hi,
Let x = # of coins per minute by machine B
Let 2x = # of coins per minute by machine A (twice as many)
Let x + 30 = # of coins per minute by machine C (30 more)
So their total output gives the equation:
2x + x + x + 30 = 246
4x + 30 = 246
4x = 216
x = 54 for machine B <== answer
2x = 108 for machine A
x + 30 = 84 for machine C
Double-check:
54 + 108 + 84 = 246
I hope that helps!! :-)
2007-07-12 16:02:41 · answer #1 · answered by Pi R Squared 7 · 1⤊ 0⤋
Here's the logic:
The slowest machine is B.
Machine B = b coins per minute.
Machine A is twice as fast as B.
Machine A = 2b coins per minute.
Machine C makes 30 more coins per minute than B.
Machine C = b + 30
All three machines together make 246 coins per minute.
Machine A's rate + B's rate + C's rate.
2b + b + (b+30) = 246 coins per minute
4b + 30 = 246 Subtract 30 from each side.
4b = 216 Divide each side by 4.
b = 54
Machine B makes 54 coins per minute.
Check:
A makes 54*2 = 108
B makes 54
C makes 54+30 = 84
108 + 54 + 84 = 246 coins per minute.
It's correct!
2007-07-12 23:10:50 · answer #2 · answered by ecolink 7 · 0⤊ 0⤋
guess and check. 54 is machine b. 108 is a and 84 is c.
(54)(2)=108(machine a) 54+30= 84(machine c)
2007-07-12 23:23:40 · answer #3 · answered by Jimmy L 2 · 0⤊ 0⤋
a + b + c = 246
a = 2b
c = b +30
2b + b + b + 30 = 246
4b + 30 = 246
4b = 216
b = 54
a = 2(54)
a = 108
c = 54 + 30
c = 84
2007-07-12 23:05:58 · answer #4 · answered by D J 3 · 0⤊ 0⤋
x+y+z = 246 ...(1)
x = 2y ...(2)
z = y+30 (3)
Replace (2) and (3) in (1)
2y+y+y+30 = 246
4y = 216
y = 54
2007-07-12 23:05:13 · answer #5 · answered by cllau74 4 · 0⤊ 0⤋