How do you translate these problems?
problem 1. find two numbers whose sum is 58 and whose difference is 16.
problem 2. the difference between two numbers is 18. the sum of twice the smaller number and three times the larger is 74. what are the numbers?
please show work
Comments
Q1:
2nd no. (y) in terms of 1st no. (x):
x + y = 58
y = 58 - x
x - y = 16
y = x - 16
1st number (x):
58 - x = x - 16
2x = 74
x = 37
2nd number (1st equation):
= 58 - 37
= 21
Answer: 37 & 21 and the numbers.
Proof (difference between them is 16):
= 37 - 21
= 16
Q2:
Smaller number (y) in terms of larger number (x):
x - y = 18
y = x - 18
3x + 2y = 74
y = (74 - 3x)/2
Larger number (x):
2(x - 18) = 74 - 3x
2x - 36 = 74 - 3x
5x = 110
x = 22
Smaller number (1st equation):
= 22 - 18
= 4
Answer: 22 and 4 are the numbers.
Proof (3 times the larger plus 2 times the smaller is 74):
= 3(22) + 2(4)
= 66 + 8
= 74
the answer for number 1 is 21 and 37
how i got this was by starting with 1 and 17 and adding them together and then 2 and 18 until i got one that equals 58. i find the best way is to do it on paper.
i'm affraid the answer to the next on is not so simple, the answer is 22 and 4.
at first i didnt get the question but when i read it carefully i finally understood it , is it similar to the first one i started with 1 and 19, 2 times 1 is 2 and 19 times 3 is 57, so then u add them together, 57 plus two is 59 which is not enough. so then i went up a few more numbersuntil i reached the correct sum, but being carefull to keep the difference to 18 i ended up with 4 times 2 is 8 and 22 times 3 is 66, added up thats 74 which is the answer.
hope this helps, srry my answer was a bit complicated
Very Simple Simultaneous Equation
Problem one
Let two unknowns be x and y
x+y = 18
x-y = 16
//elliminate the y's
-------------
2x = 34
x = 17
Now you sub
x+y = 18
//Sub x with 17
17+y= 18
y=18-17
y=1
Problem two
There are two number
Let number one be x and number 2 be y
x-y = 18 --------(Equation - 1)
3x+2y = 74 ----(Equation - 2)
//Multiply Equation 1 with 2
2x-2y = 36
3x+2y = 74
-------------------------
5x = 110
x = 22
//Now you find x just do substitution with a equation
x-y = 18 (Sub x with 22)
22-y = 18
-y = 18-22
-y = -4
y = 4
A + B = 58
A - B = 16
2A = 74, A = 37 and B = 21
-----
A - B = 18
3A + 2B = 74
2A - 2B = 36
5A = 110
A = 22
B = 4