the sum of two number is 39 . twice the first number plus 3 times the second numberis 101. find the numbers.
x+x+1=39
2x=38
x=19
twice the first number 19 it would be 38 and 57 b three times the second number. i know is wrong kind o but please tell me.
a = first number
b = second number
Conditions:
a + b = 39
2 a + 3 b = 101
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a + b = 39 Subtract b to both sides
a + b - b = 39 - b
a = 39 - b
2 a = 2 ( 39 - b )
2 a = 78 - 2 b
2 a + 3 b = 101
78 - 2 b + 3 b = 101
78 + b = 101 Subtract 78 to both sides
78 + b - 78 = 101 - 78
b = 23
a = 39 - b
a = 39 - 23
a = 16
First number = 16
Second number = 23
To solve this problem correctly, we need to set up a system of equations based on the given information.
Let's denote the first number as "x" and the second number as "y". We are given two pieces of information:
1. The sum of the two numbers is 39: x + y = 39.
2. Twice the first number plus three times the second number is 101: 2x + 3y = 101.
Now, we will solve this system of equations using the substitution method or elimination method.
Let's use the substitution method:
From equation 1, we can express y in terms of x: y = 39 - x.
Now substitute this value of y in equation 2:
2x + 3(39 - x) = 101.
2x + 117 - 3x = 101.
117 - x = 101.
-x = 101 - 117.
-x = -16.
x = 16.
So, the first number (x) is 16.
Substituting this value back into equation 1 to find the second number (y):
16 + y = 39.
y = 39 - 16.
y = 23.
The second number (y) is 23.
Therefore, the numbers are 16 and 23.