The sum of two numbers is 39. Twice the first number plus three times the second number is 101. Find the numbers.
Let's assume the first number as "x" and the second number as "y".
According to the given information:
1) The sum of two numbers is 39: x + y = 39
2) Twice the first number plus three times the second number is 101: 2x + 3y = 101
We can solve these equations by using the method of substitution or elimination.
Let's solve by the method of substitution:
1) Rearrange the first equation for x:
x = 39 - y
2) Substitute the value of x in the second equation:
2(39 - y) + 3y = 101
Simplify the equation:
78 - 2y + 3y = 101
y + 78 = 101
Subtract 78 from both sides:
y = 101 - 78
y = 23
3) Substitute the value of y in the first equation:
x + 23 = 39
Subtract 23 from both sides:
x = 39 - 23
x = 16
Therefore, the first number is 16, and the second number is 23.
To find the two numbers, let's assume that the first number is "x" and the second number is "y". According to the given information:
1. The sum of the two numbers is 39:
This can be represented by the equation: x + y = 39.
2. Twice the first number plus three times the second number is 101:
This can be represented by the equation: 2x + 3y = 101.
We now have a system of two linear equations with two variables. To solve this system, we can use the method of substitution or elimination. I will explain how to solve it using the method of substitution.
1. Solve the first equation (x + y = 39) for one variable:
We can solve for x by subtracting y from both sides of the equation:
x = 39 - y.
2. Substitute the expression for x in the second equation:
Instead of x, we'll write (39 - y) in the second equation:
2(39 - y) + 3y = 101.
3. Simplify the equation:
Distribute the 2:
78 - 2y + 3y = 101.
Combine like terms:
y + 78 = 101.
Subtract 78 from both sides:
y = 101 - 78 = 23.
4. Substitute the value of y back into the first equation to solve for x:
x + 23 = 39.
Subtract 23 from both sides:
x = 39 - 23 = 16.
Therefore, the two numbers are x = 16 and y = 23.
x + y = 39
2x + 3y = 101
x = 39 - y
2(39 - y) + 3y = 101
78 - 2y + 3y = 101
y = 23
Take it from there.