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Question 330156: 1) the greater of two numbers is 12 more than the smaller and the sum of the two numbers is 10 find the numbers
2) one number is 5 times another if 18 is subtracted from the greater the remainder will be 3 times the smaller find the numbers
3) divide 534 into three parts such that the second part will be 32 less than twice the first and the third will be 18 more than the first.
Answer by privani(34)   (Show Source):
You can put this solution on YOUR website! 1) the greater of two numbers is 12 more than the smaller and the sum of the two numbers is 10 find the numbers
Let's say the greater number=A, the smaller number=a.
Form equations:
A = a + 12.... (1)
A + a = 10.... (2)
Substitute (1) in (2):
A + a = 10
(a + 12) + a = 10
a + 12 + a = 10
12 + 2a = 10
2a = 10 - 12
a = -2/2
a = -1.... (3)
Substitute (3) in (1)
A = a + 12
A = -1 + 12
A = 11
Therefore, the greater number is 11 and the smaller number is -1.
2) one number is 5 times another if 18 is subtracted from the greater the remainder will be 3 times the smaller find the numbers
Assuming: "One number is 5 times another. If 18 is subtracted from the greater, the remainder will be 3 times the smaller. Find the numbers."
Assume: X = the greater number, x = the smaller number
Form equations:
N=5n .... (1)
N-18=3n.... (2)
Substitute (1) in (2)
N-18=3n
5n-18=3n
5n-3n=18
2n=18
n=18/2
n=9
Substitute n=9 in (1)
N=5n
N=5*9
N=45
Therefore, the greater number is 45 and the smaller number is 9.
3) divide 534 into three parts such that the second part will be 32 less than twice the first and the third will be 18 more than the first.
Assume: first part=a, second part=b, third part=c
Form equations:
a+b+c=534....(1)
b-32=2a
b=2a+32....(2)
c+18=a....(3)
Substitute (3) in (2)
b=2a+32
b=2(c+18)+32
b=2c+36+32
b=2c+68....(4)
Substitute (3) and (4) in (1)
a+b+c=534
(c+18)+(2c+68)+c=534
c+18+2c+68+c=534
4c+86=534
4c=534-86
c=448/4
c=112
Substitute c=112 in (4)
b=2c+68
b=2(112)+68
b=224+68
b=292
Substitute c=112, b=292 in (1)
a+b+c=534
a+292+112=534
a=534-292-112
a=130
So, the first part=130, the second part=292 and the third part=112.
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